Two years ago, 57 per cent of Americans held a negative outlook on the situation in Iraq, but now 30 per cent are pessimistic about the next 12 months there, the Post said.
However the poll found that views on the conflict in Afghanistan were more negative, with 51 per cent of those polled saying the war was not going well, although slightly more - 49 per cent - were optimistic about its future, compared with 47 per cent who were pessimistic.
In addition, 55 per cent of those polled said they believed the war in Afghanistan was worth fighting.
Robert Gates, the US defence secretary who is to stay on in Obama's administration, has said the US is to send thousands of troops into Afghanistan next year, and has argued that a sustained US presence is probably needed for several years.
The poll also found Bush's popularities still at record lows, with only 30 per cent of Americans approving of how Bush is doing his job in contrast to 68 per cent disapproving.
However, the numbers are a slight improvement from last month, during the US presidential campaign, when Bush's approval rating hit a low point of 23 per cent in a separate Post-ABC News poll.
The poll was conducted between December 11 to December 14 among a random national sample of 1,003 US adults, with a margin of error of plus or minus three percentage points.