The family, which has been at the centre of an international search since the sisters failed to return to Britain, was split into two groups so it could pass through the border.
The BBC said it had been passed the news by an “Islamic State smuggler in charge of some of the group’s border operations.”
He said the first group went into Syria early on Wednesday and the second on Thursday.
Sisters Khadija, Sugra and Zohra Dawood and their nine children disappeared after travelling to Saudi Arabia.
The sisters’ parents said yesterday they were “devastated by the sudden disappearance”.
In a statement, they said they did not support their actions in “taking their children into a war zone” after disappearing earlier this month.
The three sisters flew out to Saudi Arabia last month for an Islamic pilgrimage and should have returned on June 11, but were found to have flown to Turkey two days earlier.
Police said yesterday that they had received contact from one of the sisters which suggested they had travelled to Syria with their nine children, aged three to 15.
The statement said: “The parents and family members are devastated by the sudden disappearance of the three sisters and their children.
“This has caused great distress to the family and has also stopped us from living a normal life in the U.K since this incident. We are very worried about the children who could now be in a dangerous place.
“We do not support the actions of the sisters leaving their husbands and families in the UK and of taking their children into a war zone where life is not safe to join any group. We plea to anyone thinking about making a similar journey not to go.
“We are also very happy with the help and support we have had from the Police and the way they have handled the enquiry.
“Since this incident we have found it very difficult and upsetting to be in the media spotlight and would appreciate if the media let the rest of the family live a normal life as possible.
“We as family do not hold ourselves or the police responsible for the actions taken by the three sisters and ask all media companies to stop camping outside the doorstep. We ask for privacy right now as we try to cope with what has happened and hope everyone respects that.”
Earlier today, a former senior prosecutor claimed the flight of young Britons to join Islamic State is not receiving enough attention from the state or Muslim communities.
Nazir Afzal, who led the Crown Prosecution Service in north-west England from 2011 until earlier this year, said authorities should “resort to law” in cases where children are at risk of being taken to IS-controlled areas.
Mr Afzal said: “The flight of young Muslims to Isis is not getting the attention from both the state and Muslim communities it requires.
“The state needs to clarify that Foreign Office ‘advice not to travel’ is more than advice.
“The international community has judged rightly that Iraq and Syria are unsafe areas. Therefore if a child is at risk of being taken there we should, if necessary resort to law to prevent them being taken.”
Mr Afzal said this could include proceedings to make children wards of court being brought in appropriate cases.
A number of teenagers thought to be at risk of travelling to areas controlled by IS have been grounded by judges sitting in the Family Division of the High Court in recent months after social workers and police raised concerns.
Mr Afzal suggested court proceedings could also be used to stop those thought to be at risk of taking children from applying for travel documents.
“It’s the basic principle in UK law that the ‘welfare of the child is paramount’ in the Children’s Act and Universal declaration of the Rights of Child to which we are signatories,” he said.
“That means what’s in the best interests of the child, not their parents or carers.”
He added: “For adults who are supposedly capable of making their own decisions then we have to be clear what we are saying.
“Having decided that Isis is hostile to British interests, it then shouldn’t be a choice as to whether you travel. Do we really want a hostile force to receive new recruits or reinforcements?
“If the answer is no, then anyone at high risk of travelling shouldn’t just be ‘advised’ not to go, but active steps should be taken including restricting their travel where appropriate.
“Freedom of movement is a right that can be qualified by a state where crime is being prevented.”
Last year the Government outlined plans to prevent hundreds of young British Muslims from travelling to Iraq and Syria to fight with extremist militants by temporarily removing their passports.
Mr Afzal was also critical of Muslim leaders.
“The issue is only on the agenda when an individual crisis occurs,” he said. “The propaganda that Isis is delivering needs a more robust and continuing response from these leaders in order to minimise its impact on families.”
Police are “extremely concerned” about members of the missing Dawood family after receiving information that they may already be in Syria.
One of the sisters has made contact “and there is an indication that they may have already crossed the border into Syria”, West Yorkshire Police said.
Their brother is believed to be fighting for IS in Syria and he reportedly persuaded his sisters over Skype to join him.
It has emerged that the same group tried to fly earlier this year.
The North East Counter Terrorism Unit confirmed that they had been stopped and made the subject of security checks earlier this year.