At the same time, 53 percent of the respondents said the number of US troops and bombing missions should be doubled to control the insurgency, according to the poll results.
The poll was conducted by Le Moyne College and Zogby International, who interviewed 944 soldiers face-to-face at several locations in Iraq.
The pollsters said the survey had a margin of error of 3.3 per cent.
Twenty-three percent of those surveyed said they agreed with US President George W Bush's statement that US troops should stay in Iraq "as long as it takes".
In contrast, 29 per cent of the respondents said US troops should leave immediately, 22 per cent within six months, and 21 per cent within six months to a year.
Support for an exit within a year was highest among reserve and national guard troops -- 89 and 82 per cent respectively.
It was lower among regular army troops (70 per cent) and lowest among marines (58 per cent).
US mission revenge for Saddam's role in 9/11: troops
The poll found that 58 per cent of the respondents said the US mission in Iraq is clear in their minds, while 42 per cent said it is somewhat or very unclear or that they were unsure or did not understand the mission at all.
An overwhelming majority of 85 per cent said the main US mission was "to retaliate for Saddam's role in the 9/11 attacks".
Another major reason for the war cited by 77 percent of the respondents was "to stop Saddam from protecting al-Qaeda in Iraq".
Just 24 percent said that "establishing a democracy that can be a model for the Arab world" was the main or a major reason for the war.
Few saw the mission as securing oil supplies (11 per cent) or to provide long-term bases for US troops in the region (six per cent).
Ninety-three per cent said that removing weapons of mass destruction was not a reason for the US military presence in Iraq.
Asked why some Americans back home favour a rapid withdrawal from Iraq, 38 percent said it is because they are unpatriotic while 20 percent said it is because they did not think continued occupation would work.
Sixteen percent said those Americans who favoured an early exit opposed the use of the US military for a pre-emptive war, while 15 percent said it was because they did not understand the need for US troops in Iraq.
Three quarters of those surveyed were on their second or third tour of Iraq.
More than 80 percent of the respondents said they did not have a negative view of Iraqis because of insurgent attacks.
Four in five said they oppose the use of such internationally banned weapons as napalm and white phosphorous.
And 55 percent said harsh and threatening interrogation of prisoners to gain information of military value was not appropriate or standard military conduct.