The four men who have been released by UK police a day after returning from Guantanamo Bay still pose a security risk, US defence officials have said.
The four were held at Guantanamo Bay for nearly three years
Martin Mubanga, Feroz Abbasi, Richard Belmar and Moazzam Begg were reunited with their families on Wednesday night.
The men, from Birmingham and London, were freed without charge but the US says the UK has agreed to monitor them.
Azmat Begg, father of Moazzam, said his son appeared to be in "reasonably good" condition when they met.
Washington had claimed all four were "enemy combatants" who trained at camps run by al-Qaeda.
They were released after UK police concluded there was not enough evidence to charge them with any offence.
Home Secretary Charles Clarke said Britain had listened to US concerns.
The UK had negotiated a security "package" with the US and every practical step was being taken by the relevant authorities to maintain national security within the law, he told BBC News.
But under the new proposals for dealing with terrorism suspects, which he announced on Wednesday, the four men could have been placed under house arrest, he added.
The Home Office has said it will not comment on the details of what will be done to ensure the men do not pose a threat.
The Pentagon says the men were returned to Britain after the UK government promised they would not be a threat to the national security of the US or any of its allies.
But an official added: "We continue to believe that these individuals pose a significant threat."
Human rights groups have welcomed the men's release.
Amnesty International spokesman Neil Durkin said the four should not have been detained "a minute longer than necessary".
Azmat Begg declared himself "very, very pleased and glad" that his son was back in Britain.
He told BBC News he had spent three hours talking to his son before leaving him with his wife Sally and four children, one of who was born while he was in custody.
Hundreds of people have been held at Guantanamo Bay for three years
Mr Begg said Moazzam's treatment over the past three years must have "an effect" but said: "I didn't notice anything like that and it looks as though he is a very strong man".
Moazzam's mother, Gul, said she had spoken to him on Wednesday night.
She said: "I just said 'hello' and 'how are you'. He said 'I'm OK.' It's just fantastic," she said.
Louise Christian, the lawyer representing Feroz Abbasi and Martin Mubanga, said she was concerned about Mr Abbasi's condition.
She said: "He has an air of unreality about him. He doesn't know where he is."
Mr Abbasi, 24, Mr Belmar, 25, Mr Mubanga, 32, all from London, and Mr Begg, 36, from Birmingham, returned to the UK on Tuesday evening in an RAF plane.