Lord David Puttnam, a Labour peer and personal friend of Blair, said on Sunday that after months of negative headlines about Iraq, the party's electoral prospects were worsening.
The peer said it was time for the PM to make way for Chancellor Gordon Brown.
Speaking on ITV News, Puttnam said: "The prime minister is synonymous with Iraq, and Iraq will only deliver bad news. If I were him, I would go before the summer recess."
Blair's support for the war in Iraq, a U-turn on a referendum on a European Union constitution and an immigration policy widely seen as bungled have crushed public trust and prompted speculation that Brown will take over.
An opinion poll on Sunday spelled further bad news for Blair.
The YouGov poll in the Mail on Sunday said Labour could only win an overall majority at the next election if the prime minister made way for Brown.
The poll also showed support for the war in Iraq at an all time low after charges of abuse of Iraqi prisoners by British and American troops.
Puttnam's choice as next Labour
PM, Gordon Brown
Puttnam, a renowned film producer, added that Brown would "inevitably" be the man to take over.
"Gordon Brown is exactly the person who will at least be able to think that we focus things on the domestic agenda. And I suspect he would be able to win quite comfortably at a general election were it to be held within the next 12 months."
The YouGov poll showed Labour would win the election, but fall short of a majority with Blair in charge. But it would win a majority of 77 seats if he handed over to Brown.
YouGov questioned a representative sample of 1976 electors online between Thursday and Saturday.