Blair confirmed that he had personally asked President Bush to free the remaining four Britons detained in the camp.
He said Washington continued to insist, however, that the British government must guarantee the men will not pose a threat, either to Britain or elsewhere in the world.
"Guantanamo Bay is an anomaly that has at some point got to be brought to an end," Blair told a committee of lawmakers.
"The American response has been the same all the way through. At the end if the trial requirements do not meet our standards then they will come back, but we also have to make sure that they will not be a threat either to this country or elsewhere," he added.
Five other Britons who spent up to two years in U.S. custody at the base were released to British officials in March, and were soon freed without charge.
London is still locked in discussions with Washington over the detention of four other Britons held at Guantanamo: Moazzam Begg, 36; Feroz Abbasi, 23; Richard Belmar, 23; and Martin Mubanga, 29.
Begg and Abbasi are listed as some of the first detainees likely to face a military commission there. Last week, Britain's Attorney General, Lord Goldsmith, said the commission would not provide a fair trial by international standards.
According to court papers seen by The Associated Press, Blair has personally asked Bush to allow the four Britons to return home.
Blair confirmed to the House of Commons Liaison Committee (search) that he had personally raised the issue with Bush a few weeks ago.
"I do not think the United States is being unreasonable in saying we need to make sure there is proper security in place for these people," Blair told the committee. "I hope we can resolve it reasonably soon."
Blair is under pressure from political opponents and many of his own governing Labour Party (search) lawmakers to resolve the issue. Some suggest the deadlock reveals he actually wields little influence in Washington, despite supporting Bush in the Iraq war.