According to an opinion poll published on Saturday, 51% of respondents agreed it was "now time for Tony Blair to resign and hand over to someone else".
Only 35% of respondents gave a definite "no" to the question, the poll for The Independent newspaper showed.
The findings end a difficult week for the prime minister, which saw him forced to order an investigation into whether there were failures of intelligence before the war.
The poll also found that 54% thought Blair lied to Britain about the threat posed by Iraq's alleged weapons of mass destruction before the campaign last year to remove Saddam Hussein.
Blair faces mounting political pressure about the fact that no stocks of chemical or biological weapons have been found in Iraq, nine months after the fall of Baghdad.
Tories led by Michael Howard are
gaining from anti-Blair backlash
Before the war, the prime minister insisted to a sceptical country it was correct to join the US-led conflict because Saddam's arsenal of illegal weapons posed an immediate threat to the West.
The telephone poll of 1003 people showed the main opposition Conservative Party has benefited from the backlash against Blair, with 36% of people backing the Tories against 35% for Blair's Labour Party.
On Tuesday, Blair announced a former head of the civil service would lead an inquiry into pre-war information about Iraq's weapons of mass destruction.
However Saturday's poll showed 68% of people believe the probe will end up being a "whitewash".
Similar charges were levelled against a report by judge Lord Brian Hutton, who at the end of last month exonerated Blair's government of deliberately exaggerating a dossier on Iraq's weapons.
Hutton instead lambasted the BBC for reporting that a claim Iraq could unleash chemical or biological weapons within 45 minutes had been inserted by ministers even though they knew it was wrong.
However, even this issue has returned to haunt Blair.
On Wednesday, Blair was ridiculed by critics after admitting when the 45-minute claim was made, he had no idea whether it referred only to short-range "battlefield" weapons or also to missile-launched devices.