The hundreds of military deaths in the year since Bush declared major combat over, the failure to find weapons of mass destruction and the fraying of the occupation have all shaken many Americans.
But until recently a majority had shown confidence in Bush, who faces a presidential election in six months.
According to a New York Times/CBS poll published on Thursday, however, the number of Americans who feel the 20 March 2003 invasion was justified has fallen to 47%, from 58% a month ago and 63% in December.
Approval of Bush's handling of Iraq has dropped to 41% from 49% last month and 59% in December.
Bush's overall approval rating dropped to 46%, the lowest of his presidency and three percentage points lower than last month. It was 89% after the September 11 attacks, and 71% at the start of the Iraq invasion.
"...Americans have become much less positive about both the rationale for the war and about the way the war is progressing"
In the polls, 46% said the US should have stayed out of Iraq, up from 37% a month ago while 58% said the results of the invasion were not worth the loss of American lives, up from 54% a month ago.
A USA Today/CNN/Gallup poll of 3,444 Iraqis released on Thursday showed they were growing weary of the occupation, with 57% wanting the US-led occupation out immediately, despite fears it could place them in greater jeopardy.
While 61% of Iraqis felt the invasion to oust Saddam Hussein as president was worth it, 46% said it did Iraq more harm than good.
But polls do not show a major swing of support for Democratic presidential contender John Kerry as events in Iraq worsen.
A Gallup poll released this month found that 48% of adults supported the Republican president, while 46% supported John Kerry.
"Over the last 12 months, Americans have become much less positive about both the rationale for the war and about the way the war is progressing," the Gallup organisation said.
"Yet even now, there is a majority (albeit a bare majority) who support the basic concept of the US presence in Iraq. As long as that majority holds, Bush will continue to be able to hold off his critics," it added.