David Cameron today challenged the prime minister to agree to a vote in the House of Commons on the replacement of Trident nuclear weapons.
At prime minister's question time this afternoon, he also likened Mr Blair to BBC sitcom character David Brent - "utterly redundant, just hanging around the office" - and pressed him over forthcoming world trade talks.
Mr Blair responded by taunting Mr Cameron over his plan for a British bill of rights to replace the Human Rights Act, which was criticised by former Conservative chancellor Ken Clarke.
The Conservative leader began by attempting to exploit the supposedly different lines on Trident coming from Mr Blair and the chancellor.
According to Mr Cameron, Gordon Brown had said there would be a vote on replacing Trident.
Mr Blair replied that Trident was a manifesto commitment on which a decision would be taken later this year, when "we will of course consult the house fully".
Pressed further the prime minister said: "We will announce the means of consultation at the time we publish the white paper. Of course we believe it is important we have the fullest possible debate on the subject."
Citing the alleged difference of opinion between Mr Brown and Mr Blair, the Tory leader replied: "Isn't there a danger that the prime minister is becoming the David Brent of Downing Street - utterly redundant, just hanging around the office?"
Mr Blair's response was to taunt Mr Cameron over his new plan to scrap the Human Rights Act, which was described as "xenophobic" by Ken Clarke, who heads up the Tories' Democracy Task Force.
"I'm surprised when he's just announced a major change to the British constitution he doesn't want to get up and debate it."
He continued: "Direction is about policy. I am happy to debate our policies, I am happy to debate his policies. I am happy to have a debate," he said.
"He has got two questions left, let's debate policy," he added to cries of "you're scared Cameron - get back up" from the Labour benches.
Their later exchange focused on the world trade talks in Geneva, with Mr Cameron asking how confident the prime minister was on making progress at the G8 talks.
Mr Blair said he was working hard to achieve progress, and would be pushing for further movement on agricultural tariffs from the G20 and on subsidies from the US.
Liberal Democrat leader Menzies Campbell asked the prime minister about the hostage situation in the Middle East - involving an Israeli soldier kidnapped by Palestinian gunmen - and whether he had discussed it with the US president.
With the apparent willingness of Hamas to accept a "two-state solution", Sir Menzies said the Middle East peace process was at a "particularly crucial moment".
Mr Blair said the Middle East formed "a major part of any conversation" he had with the US president. He added that if Hamas was prepared to commit to a two-state solution - which meant they were committed to the existence of Israel and the renunciation of violence - then the peace process should be taken forward as quickly as possible.
The prime minister was also given a taster of the difficulties he faces within his own party over the replacement of Trident.
Islington North Labour MP, Jeremy Corbyn, a longstanding member of the Campaign for Nuclear Disarmament, asked why the government was even considering replacing the UK's nuclear deterrent.
Mr Blair said the question showed the debate on the subject would be a lively one.