Mr Blair sought to defend his previous claims of contact between the two as a British intelligence report, seen by BBC News, indicated that there were "no current links" between them.
"
If we had a relationship with al-Qaeda and we believed in that
relationship, we wouldn't be ashamed to admit it
"
Saddam Hussein
The classified document, written three weeks ago, says there has been contact between the two in the past, but that the relationship had foundered due to mistrust and incompatible ideologies
That conclusion contradicts one of the charges laid against Iraqi leader Saddam Hussein by the United States and Britain - that he has cultivated contacts with the group blamed for the 11 September attacks.
Weakened case?
Mr Blair, who will meet UN weapons inspection chief Hans Blix on Thursday, told MPs there were "unquestionably" links between al-Qaeda and Iraq.
"But how far the links go is a matter for speculation," he said.
Liberal Democrat leader Charles Kennedy said the government's case for war against Iraq would "undoubtedly be weakened, if not fatally undermined by talking up links between al-Qaeda and Iraq which are not there".
Current Security Council
But Mr Blair insisted: "It would be unfair to say we have talked up these links. We do not make our case against Saddam and Iraq on the basis of links with al-Qaeda ...
"I do not think it's fair to suggest that we are trying to push this in some way as a cover for any lack of argument on weapons of mass destruction.
"I believe our case on weapons of mass destruction is very, very clear indeed."
Earlier, Downing Street appeared to play down its past assertion that Saddam Hussein's regime was "sheltering" al-Qaeda "operatives".
A spokesman said Tony Blair's statements on the issue reflected the advice he's received from the Joint Intelligence Committee, and argued "we've not pushed the envelope out over this - we've been measured".
Foreign Secretary Jack Straw also sought to back up Mr Blair's line by insisting that intelligence had shown the Iraqi regime appeared to be allowing a "permissive environment" "in which al-Qaeda is able to operate".
Tony Benn
The defence intelligence staff's report emerges even as Washington was calling Saddam a liar for denying, in a television interview with former Labour MP and minister Tony Benn, that he had any links to al-Qaeda.
It also comes on the day US Secretary of State Colin Powell goes to the United Nations Security Council to make the case that Iraq has failed to live up to the demands of the world community.
"
I personally had not believed that the Iraqi regime could be this stupid
"
Jack Straw
Mr Straw is also ratcheting up the rhetoric in the ongoing crisis saying the use of force to reinforce the will of the UN to get Saddam to disarm was now "more probable".
He said he could not believe the Iraqi regime would be "this stupid" not to disarm.
'Politicised intelligence?'
The defence intelligence staff document, seen by BBC defence correspondent Andrew Gilligan, is classified Top Secret, but the prime minister insisted: "I did not see it - it was not part of the reports given to me."
The brief says al-Qaeda leader Osama Bin Laden views Iraq's ruling Ba'ath party as running contrary to his religion, calling it an "apostate regime".
"His aims are in ideological conflict with present day Iraq," it says.
Mr Gilligan says that in recent days intelligence sources have told the BBC there is growing disquiet at the way their work is being politicised to support the case for war on Iraq.
He said: "This almost unprecedented leak may be a shot across the politicians' bows."