The poll was conducted by the Los Angeles Times newspaper and published on Friday.
The survey indicates for the first time that a majority of voters doubt whether the situation in Iraq was worth the cost of US military involvement.
In the survey of 1,230 registered voters conducted across the country from Saturday through Tuesday, 53% said it was not worth going to war in Iraq while 43% said it was and 4% said they did not know. The sample has a margin of error of three percentage points.
In a March LA Times survey 53% of voters said the war was worth fighting and 43% said it was not, a reverse of the current figure.
The paper said that 35% of American voters thought the US was making good progress in Iraq while 61% said the country was getting bogged down there.
But 52% of voters said that they thought the United States was winning the war in Iraq and less than one in four said the insurgents were winning.
Despite a growing sense that the war was not justified, voters did not advocate a quick pullout of Iraq.
Less than 20% said America should withdraw its troops within weeks. Seventy-three percent said that there should be no specific date for withdrawal because disorder and civil war could result.
Fifty-five percent of voters said they disapproved of President George Bush's handling of the war, while 44 percent approved.