It would be "very, very surprising" if the two sets of London bombings in July were not connected, Home Secretary Charles Clarke has told the BBC.
But Mr Clarke said there was "not a direct linkage formally established".
His comments come after he reiterated that he remained "worried" about the possibility of further attacks.
On Monday he held talks with Met Chief Sir Ian Blair, who has said the fact there were two attacks made further bombs "more, rather than less" likely.
Mr Clarke was asked on BBC Radio 4's Today programme if any link had been established between the 7 July and 21 July attackers.
"I think it would be very, very surprising if they weren't linked in some way, but evidence is an issue," he said.
"There is not a direct linkage formally established, to be able to make that assertion directly."
Mr Clarke said police and security services were working to establish what support, training and other assistance had been provided to the two groups of bombers.
"We remain worried. The [Metropolitan Police] commissioner has been very clear throughout that it would be ridiculous for us to assume that a further act would not take place.
"Obviously, one of the main purposes of the investigation - which is rolling ahead very strongly at the moment - is to identify any linkages which would help us act more effectively to be able to reduce that likelihood - and that work is happening," Mr Clarke said.
"The police, together with the other security services, are doing an excellent job.
"But it would be absolutely foolish for me, or for anybody else to say that we've eliminated the risk. We haven't."
Mr Clarke made clear there was no intelligence available of any specific threat of a new terrorist attack.
"But we are working on the basis that the people who organised these attacks could proceed with other attacks as well.
"And that seems to me the only rational basis on which we should proceed."
On Monday Metropolitan Police chief Sir Ian Blair said: "The fact that there's been two attacks makes it more, rather than less likely that there'll be further attacks.
"I mean, that's just the logic of all this, but we of course are working incredibly hard with the intelligence services to prevent it".
In other developments, Mr Clarke said he wanted the legal process to deport 10 people deemed to pose a threat to national security to take as "little time as possible".
"Those individuals concerned are now under detention, pending deportation, and that means they are removed from any particular ability to threaten us in that way. That is a very important step."
His comments came as New York-based Human Rights Watch said the UK could not legally deport suspects such as radical cleric Abu Qatada to Jordan despite a promise they will not be tortured.
The civil rights group says it would be breaking international law if the UK deports suspects to a country where torture is a "serious risk".