It emerged on Monday that two of the London bombers - Mohammed Sidique Khan and Shehzad Tanweer – met with the ringleader of the fertiliser plot.
Mr Cameron asked the prime minister whether he had "ruled out" a fresh inquiry by an independent body.
Replying, Mr Blair said that the parliamentary intelligence and security committee had already conducted an exhaustive investigation into MI5's knowledge about the terror suspect's movements in the build-up to July 7th.
He said a new, independent inquiry would "undermine support for the security services" and divert resources away from the fight against terrorism in the UK.
Today's calls follow those made yesterday by survivors of the July 7th bombings, which killed 52 people.
A letter delivered by survivors to home secretary John Reid said an inquiry could be used to "examine issues aimed at saving lives, minimising suffering and improving the response of government agencies to the continuing threat of terrorist attacks".
Three people are currently awaiting trial in connection with the attacks.
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