One of the men was detained following searches of an address in the Withington area of the city, while another was arrested in a part of Greater Manchester that was not disclosed.
A woman arrested in the Blackley area of Manchester on Wednesday has been released without charge.
The investigation into the Manchester Arena atrocity has continued apace as security agencies swooped on the suicide bomber’s suspected “network”.
On Wednesday, a series of raids were executed across Manchester, Wigan and Nuneaton, Warwickshire, while relatives of bomber Salman Abedi were detained in Libya.
In the early hours of Thursday morning, counter-terror police carried out a controlled explosion at a property in the Moss Side area of Manchester, although no arrests were reported by police.
Abedi’s father, Ramadan Abedi, was arrested in Tripoli with his brother Hashim, who Libyan security forces said was “aware of all the details” of the attack.
A 23-year-old man - named in reports as Abedi’s older brother Ismail - was detained in Chorlton, south Manchester, on Tuesday.
Ramadan Abedi had earlier claimed his son Salman was innocent, saying: “We don’t believe in killing innocents. This is not us.”
The developments came as the police investigation was hit by further leaks to the US media, with the New York Times releasing crime scene photos appearing to show bomb fragments and the backpack used to conceal the explosive.
The National Police Chiefs’ Council (NPCC) said the leak of the pictures breached trust and “undermines our investigations and the confidence of victims, witnesses and their families”.
Prime Minister Theresa May is expected to raise UK concerns when she meets US President Donald Trump at a Nato meeting in Brussels on Thursday.
Twenty-two people were killed and dozens seriously injured when Abedi, 22, detonated a device as fans left an Ariana Grande concert on Monday night.
With Britain on critical alert for further attacks:
• Two men were arrested in Manchester in the early hours of Thursday morning, one in the Withington area.
• Detectives carried out a controlled explosion as they searched a property in the Moss Side area of Manchester in the early hours of Thursday.
• Three men were arrested after police executed warrants in south Manchester, while officers entered an address in the city centre using a controlled explosion on Wednesday afternoon.
• Two further arrests included a man carrying a suspect package in Wigan and a man at an address in Nuneaton, Warwickshire.
• Sky News said it had obtained CCTV images which showed Abedi at Manchester’s Arndale shopping centre on Friday after he bought the rucksack used in the attack.
• Cheshire Police confirmed that one of its female officers died while off-duty at the concert but have not named her.
• Almost 1,000 military personnel were being deployed around the country, including to key sites such as Parliament, Buckingham Palace and Downing Street, after the official terror threat assessment was raised to critical, the highest level, indicating that a further attack may be imminent.
• France’s interior minister disclosed that the bomber is believed to have travelled to Syria and said he had “proven” links with Islamic State (IS), which has claimed the attack.
• Claims emerged in America, reported by NBC News, that members of the bomber’s family had warned security officials Abedi was “dangerous”.
• Management for US singer Grande, whose concert had just finished when the bomb went off, said her world tour including upcoming gigs at the O2 in London had been postponed.
• The Government announced that a minute’s silence will be held at 11am on Thursday in remembrance of those who died or were affected by the attack.
The bombing was the deadliest terrorist incident to hit the UK since the July 7 attacks in London in 2005 and sparked a nationwide security operation amid fears further strikes could be imminent.
Greater Manchester Police Chief Constable Ian Hopkins said: “I think it’s very clear that this is a network that we are investigating and as I’ve said, it continues at pace, this extensive investigation is going on and activity taking place across Greater Manchester as we speak.”
The force said it was “confident” it had identified every victim but they would not be formally identified until after post-mortem examinations were completed in four to five days.
There were reports that members of the public reported Abedi to the anti-terrorism hotline several years ago.
An unnamed Muslim community worker told the BBC two people who knew the attacker at college tipped off officers after he made statements “supporting terrorism” and expressing the view that “being a suicide bomber was okay”.
The calls are thought to have been made five years ago after Abedi left school, the community worker added.
Mrs May will chair a fourth meeting of the Government’s Cobra emergency committee since the Manchester attack, on Thursday morning, Downing Street said.
In response to the heightened threat, the Government has activated Operation Temperer, providing up to 3,800 troops to support the police in security operations.
Home Secretary Amber Rudd said 984 military personnel were being deployed around the country, which the Metropolitan Police said had freed up 1,000 armed officers to carry out patrols.
She confirmed Abedi had recently returned from a visit to Libya, and said the nature of the attack suggested he may have had support.
A spokesman for Libyan authorities said one of Abedi’s final acts before the murders was to ring his mother.
He told BBC2’s Newsnight: “His brother felt there was something going on there in Manchester and he thought his brother would do something like bombing or attack. So after that, he told us, ‘Having internet, I see the attack in Manchester and I knew that’s my brother’.”
The spokesman added that Libyan authorities were aware of Abedi going to the capital of Tripoli on April 18 and believed he stayed for two or three weeks.
He revealed that Abedi’s younger brother Hashim had been investigated for about a month and a half over suspicions that he was linked to IS.
“We were not quite sure about this, but when we arrested and we asked him, he told us, ‘I have ideology with my brother’. Hashim told us, ‘I know everything about my brother, what he was doing there in Manchester’.”