It also comes as armed men attacked the convoy of Iraq's vice-president and as up to 30 Iraqis were kidnapped in Baghdad on Thursday.
NBC reported that only 23 per cent of respondents backed the president's strategy, representing an 11-point drop since the last NBC poll in October.
Nearly seven in 10 respondents said they felt less confident the war would come to a successful conclusion, NBC said. Fifty three per cent said the US did not have an obligation to killed or wounded American soldiers to remain in Iraq.
'Very poor' government
Bush has said he is considering options for changing US policy in Iraq following the results of the bi-partisan Iraq Study Group report, but has said he will not be rushed into any decision.
Nearly 66 per cent of respondents to the Iraqi survey thought violence would decrease if US forces were to leave.
Thirty-eight per cent were also "unconfident" that Nuri al-Maliki, the Iraqi prime minister, would be able to improve the situation in Iraq and nearly 90 per cent described the government's implementation of its commitments and promises as very poor.
Of the respondents, 36.5 per cent said they felt the official security forces were unable to keep control in the country.
Meanwhile, the security situation deteriorated even further on the ground in Iraq when about 100 armed men wearing military uniforms kidnapped dozens of merchants in a busy commercial street in the centre of Baghdad.
Witnesses and security officials said the men arrived in about 20 silver sports utility vehicles and grabbed between 20 and 30 people in the Sinak commercial area of Rashid Street.
In another incident in the capital on Thursday the convoy of Adel Abdul Mahdi, the vice president, came under attack, but there were no immediate reports of any injuries.
Officials from the interior ministry said Abdul Mahdi was in the convoy but unhurt.