“I think it would be very, very surprising if they weren’t linked in some way, (but) there is not a direct linkage yet formally established to be able to make that assertion,” said Home Secretary Charles Clarke, speaking on BBC radio.
The comments come a day after Mr Clarke, the cabinet minister in charge of public security, was briefed on the status of investigations by London Metropolitan Police chief Sir Ian Blair.
He said there is no evidence “in the judicial sense” that those behind the July 7 and 21 attacks were linked.
While he pointed out that police have made great headway in gathering forensic evidence, they are a long way from determining the extent of the networks behind the attacks.
Four apparent suicide bombers were among 56 people who were killed when blasts hit three underground trains and a double-decker bus on July 7.
“It’s obvious that there was a group that worked on July 7 and another group that worked on July 21,” said Mr Clarke.
“The extent to which they had support, training, induction, even tasking from outside the groups of people who actually committed the attacks themselves is something which is being investigated very, very fully and comprehensively.”
“The full international links in relation to all this remain to be fully clarified,” he said.
Earlier, Mr Clarke told reporters the risk of further attacks remains.
“It would be foolish for me or for anyone to say that we’ve eliminated the risk. We haven’t. The risk needs to be contested, and that’s what we’re doing,” he said.
While he said there is no evidence to suggest the existence of a third cell that might carry out attacks, “we’re working on the basis that the people who organised these attacks could proceed with other attacks as well”.
A total of 39 people have been arrested in the wake of the attacks, including three prime suspects in the failed July 21 attacks, who have been charged with attempted murder, conspiracy and possessing explosives.
Ten foreigners have meanwhile been detained pending deportation on grounds of national security.