The poll, which shows that views on the Iraq war represent a divide between Republicans and Democrats, reveals that 53% of voters say that the situation in Iraq did not merit the war, while 43% say it did. When the question was asked by the same pollsters in November and March the figures were reversed.
Meanwhile, only 35% believe the US is making good progress, while 61% feel America is "getting bogged down".
Conducted on the weekend that saw the final details of the unanimous United Nations security council vote to endorse the June 30 handover, the polling results are grim news for President George Bush. Results from the same poll on Thursday showed his Democratic party challenger, John Kerry, extending his national lead over the president, although Mr Bush was faring better in swing states.
Among those who think the threat from Iraq justified war, Mr Bush leads Mr Kerry, the presumptive Democratic presidential nominee, 83% to 13%. Among those who think the war was not justified, Mr Kerry leads, 84% to 11%.
Three-fifths said Mr Bush's Iraq policies had hurt America's image abroad; one in five thought they had improved attitudes toward the US.
But if the survey revealed that Mr Bush was in trouble it was not all good news for Mr Kerry, with whom many voters have yet to positively identify. In a sign that Mr Kerry's position is murky to many voters, the poll found 15% said he had offered a clear plan on how to handle the situation, while 34% said he had not, and the rest did not know.