The council's secretary general Harun Khan said he expected authorities to step up security "as a matter of urgency", adding many would feel "terrorised" following the incident outside the Muslim Welfare House in Seven Sisters Road.
He said: "According to eyewitness accounts and videos taken after the incident, it appears that a white man in a van intentionally ploughed into a group of worshippers who were already tending to someone who had been taken ill.
"We do not know how many were injured or killed, but our prayers are with the victims and families.
"During the night, ordinary British citizens were set upon while they were going about their lives, completing their night worship. It appears from eyewitness accounts that the perpetrator was motivated by Islamophobia.
"Over the past weeks and months, Muslims have endured many incidents of Islamophobia and this is the most violent manifestation to date.
"Given we are approaching the end of the month of Ramadan and the celebration of Eid with many Muslims going to local mosques, we expect the authorities to increase security outside mosques as a matter of urgency.
"Muslim communities have been calling for increased action to tackle the growth in hate crime for many years and transformative action must now be taken to tackle not only this incident but the hugely worrying growth in Islamophobia.
Many will feel terrorised, no doubt be angry and saddened by what has taken place tonight.
"We urge calm as the investigation establishes the full facts, and in these last days of Ramadan, pray for those affected and for justice."
Mohammed Shafiq of the Ramadhan Foundation, a Muslim organisation which speaks out against extremism, said: "I utterly condemn the senseless and evil van attack against Muslim worshippers outside the Finsbury Park Mosque in London.
"According to eyewitnesses this was a deliberate attack against innocent Muslims going about their life.
"We should make clear that if this attack is confirmed as a deliberate terrorist attack then this should be classed as an act of terrorism.
"The British Muslim community requires all decent people to stand with us against this evil violence.
"Rampant Islamaphobia has been on the rise for a number of years and those on the far right have perpetuated hatred against Muslims.
"They should be called out for their hatred.
"The days ahead will be difficult, but with unity and tolerance we will prevail. We will not allow these far right extremists to divide our diverse communities.
"Enough is enough, my condolences and prayers for all the victims and their families. They are in my prayers."
Labour leader and local Islington North MP Jeremy Corbyn expressed his shock at what had happened, writing on Twitter: "I'm totally shocked at the incident at Finsbury Park tonight.
"I've been in touch with the mosques, police and Islington council regarding the incident. My thoughts are with those and the community affected by this awful event."
Meanwhile, chairman of the mosque at Finsbury Park, Mohammed Kozbar, tweeted: "Our thoughts and prayers with those who got injured and effected by this cowardly attack in Finsbury Park area, many casualties in the floor."
The widower of murdered MP Jo Cox spoke out on Twitter as news of the attack broke, saying that the far right and Islamist terrorists shared an ideology and both must be defeated.
Brendan Cox tweeted: "Far right facists&Islamist terrorists are driven by same hatred of difference, same ideology of supremacy&use same tactics.We'll defeat both.
"When islamist terrorists attack we rightly seek out hate preachers who spur them on. We must do the same to those who peddle Islamophobia".
Mother-of-two Mrs Cox, who represented the Batley and Spen conctituency in West Yorkshire, was shot and stabbed as she arrived for a constituency surgery in Birstall on June 16 last year.
Right-wing loner Thomas Mair was given a whole life term at the Old Bailey in November after being convicted of her murder.
The attack happened after a weekend of events as part of The Great Get Together, which saw communities across the country get together to mark the anniversary of the Labour MP's murder with positivity.
London Mayor Sadiq Khan urged people to "remain calm and vigilant".
He said: "We don't yet know the full details, but this was clearly a deliberate attack on innocent Londoners, many of whom were finishing prayers during the holy month of Ramadan.
"While this appears to be an attack on a particular community, like the terrible attacks in Manchester, Westminster and London Bridge it is also an assault on all our shared values of tolerance, freedom and respect.
"The situation is still unfolding and I urge all Londoners to remain calm and vigilant. Please report anything suspicious to the police, but only call 999 in an emergency.
"The Met have deployed extra police to reassure communities, especially those observing Ramadan."
Home Secretary Amber Rudd said: "My thoughts are with all those affected by the appalling incident at Finsbury Park.
"I am in contact with the Metropolitan Police who have confirmed it is being investigated by their Counter Terrorism Command.
"We must all continue to stand together, resolute, against all those who try to divide us and spread hate and fear."
Labour's shadow home secretary Diane Abbott, whose Hackney North and Stoke Newington constituency lies close to the scene, called for police to review security at mosques.
She tweeted: "Terror attack outside #FinsburyPark mosque. Police must urgently review security for all mosques #StandTogether."
Green Party co-leader Caroline Lucas said her thoughts were with the community and emergency services, adding: "We will not be divided."
Muhbeen Hussain, founder of British Muslim Youth, said: "We strongly condemn this horrendous suspected terrorist attack and pray for the innocent victims and their families that have been affected by this incident.
"I have personally visited the scene of the attack and spoke to many eyewitnesses, many of whom were quite emotional after witnessing a murder and seeing many people being injured.
"There were also high emotions as many witnesses saw this as a deliberate attack on Muslims.
"Other reports even suggest that the individual that has now been arrested for the incident was taken under citizen arrest by many of the Muslim worshippers at the scene and handed over to the police.
"I have also heard that this individual was shouting, 'I want to kill all Muslims'.
"In less than a month, we have witnessed horrific attacks in Manchester, London Bridge, Borough Markets, a tragedy at Grenfell Tower and now this horrific attack.
"We as communities stood united in all of these difficult times and we must come together once more.
"I also urge anyone that has further information to speak to the police, so they have as much information as possible to deal with the on-going investigation."
Rabbi Herschel Gluck, president of Shomrim, a Jewish neighbourhood watch group, was at the police cordon to show "solidarity" with the community.
He told the Press Association: "We have very good community relations here.
"(My reaction was) deep shock and deep concern about the ramifications of this terrorist atrocity.
"On one hand, I feel the people deeply appreciate our presence here and feel reassured that we are here with them, but on the other hand a lot of anger and frustration that members of their community have been attacked."
Fiyaz Mughal, the founder of Tell Mama, which works on tackling anti-Muslim hatred, said there had been an increase in anti-Muslim sentiment in recent weeks.
He told BBC Radio 4's Today programme: "The way it works is pretty much there are very large spikes or spikes, we call them measurable spikes, after major terrorist incidences, so Islamist extremist incidences create the largest spikes we see.
"We saw that very clearly after Manchester, a very high peak, we saw that clearly after London Bridge, we didn't see it after Westminster.
"So the answer to that is yes, these peaks of anti-Muslim hate incidences reported in do go up in very high numbers after terrorist incidences."
The chief constable of Greater Manchester Police has tweeted his sympathy for the community caught up in the Finsbury Park attack.
Ian Hopkins wrote: "#finsburyattack such awful news. The victims & their families are very much in my thoughts and prayers."
It was less than a month ago that terrorist Salman Abedi detonated a suicide bomb killing 22 people, including children, after an Ariana Grande concert at Manchester Arena.
French President Emmanuel Macron tweeted: "Thoughts for London and victims after this new ordeal."
London Mayor Mr Khan later told BBC Radio 4's Today programme: "Terrorism is terrorism, whether it's Islamist-inspired or inspired by others.
"London has been through an extremely difficult time, it's been a tough few weeks, but I'm so confident that we're going to come through this, we'll be strong, we'll stay strong and we won't allow these people to divide us."
Mr Khan also warned about indoctrination of extremists on the internet.
In a statement posted on its website, the Finsbury Park Mosque said it "condemns in the strongest terms a heinous terrorist attack".
"The van driver deliberately mowed down Muslim men and women leaving late evening prayers from Finsbury Park Mosque and Muslim Welfare House just after midnight," the statement said.
"This is a callous terrorist attack, which coincides with the murdered MP, Jo Cox, anniversary."
The mosque's chairman, Mohammed Kozbar, described the incident as "a cowardly attack which is no different than the attacks in Manchester and London".
"Our community is in shock, our thought and prayer with those who have been affected by this," he said.
The statement added: "Finally, our thoughts and prayers are with the victims and their families.
"We urge all attending mosques and going about their business to remain vigilant in this difficult time."
Dr Moshe Kantor, president of the European Jewish Congress, said: "This is an unconscionable attack on Muslim worshippers during their holy month of Ramadan.
"We condemn this attack and its attempt to escalate tensions in the UK and we stand firmly besides our Muslim brothers and sisters in the aftermath of this attack.
"An attack on one religion is an attack on all religions and all people and faiths must stand together against terror."
The Muslim Welfare House praised the bravery of its imam, Mohammed Mahmoud, who helped to calm the situation as members of the public detained the attacker.
A statement posted on its website said the organisation had hosted a Great Get Together event in the memory of murdered MP Jo Cox for all faiths a few days ago and that the Muslim community in the area is "horrified" and "shocked" by Monday's incident.
"We have worked very hard over decades to build a peaceful and tolerant community here in Finsbury Park and we totally condemn any act of hate that tries to drive our wonderful community apart," it said.
"We would appeal for calm at this time. It is unhelpful for there to be speculation about the incident. All of our efforts should be towards getting justice for the victims and ensuring our community stays the diverse, tolerant and welcome place we know it to be. We call on all, including the media, to act responsibly at this time.
"We have already met with the police, council and our local MP, Jeremy Corbyn. We would like to thank them for their support.
"Our mosque and welfare centre provides vital support to many people in north London and we will continue to do this despite this incident.
"Muslim Welfare House has always welcomed the whole community. Only a few days ago we hosted a Great Get Together in memory of Jo Cox, attended by people of every faith and background.
"I would like to particularly thank our imam, Mohammed Mahmoud, whose bravery and courage helped calm the immediate situation after the incident and prevented further injuries and potential loss of life."
Environment Secretary Michael Gove said he was sure the Prime Minister would be "distraught" about the attack.
He told Sky News: "I know she will feel, as I do and as the Home Secretary does, absolutely distraught about the human suffering here.
"The Prime Minister has always, during her time as home secretary and as Prime Minister, put keeping communities safe at the heart of everything she does. I know she will have been talking to the security services, to the police and to others to make sure that every step necessary is taken.
"I'm sure that later today we will hear more from the Prime Minister and Government about the next steps that need to be taken to reassure people that we are keeping them safe and to get to the bottom of this disgusting crime."
Bhai Amrik Singh, chairman of the Sikh Federation UK, said: "The incidents in the last three months suggest there needs to be an honest dialogue and a fundamental shift in the way government tackles all forms of hate and terror.
"Hate and terror must be stamped out by directly confronting all those who promote an ideology and philosophy based on hate and terror.
"Sikh teachings, history and the Sikh way of life offers not only hope, but direction on how to tackle hate and terror. Those making policies in governments across the globe need to draw upon belief systems and thinking designed to deal with hate and terror head on."
Outgoing Liberal Democrat leader Tim Farron said: "The Finsbury Park attack is senseless barbarism. Yet again we are rocked by a horrific incident for which there is no rhyme or reason.
"People who commit these heinous acts want to divide us, force us to turn in on ourselves and fight each other. We cannot and must not let them win. Our values matter, we must stand together.
"My deepest sympathies are with the victims and their families.
"I would like to pay tribute to the bravery and dedication of the emergency services, who, yet again, have gone above and beyond to help those in need.
"In these moments while others run in the opposite direction, our emergency services run towards danger."
Imam Qari Asim, a member of the Government's anti-Muslim hatred working group, said: "It's important that we seek out those who incite hatred, of whatever form, to challenge and condemn their vile actions. There can be no tolerance of religious hatred in our country.
"Given that there has been a five-fold increase in anti-Muslim hatred since the London Bridge attack, Muslims are deeply concerned and anxious about growing levels of Islamophobia.
"But we must remain calm and vigilant, and increase security around mosques. We must stand together to drown out extremism and hatred with hope and unity."