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WASHINGTON (CNN) -- Opposition among Americans to the war in Iraq has reached a new high, with only about a third of respondents saying they favor it, according to a poll released Monday.

Just 35 percent of 1,033 adults polled say they favor the war in Iraq; 61 percent say they oppose it -- the highest opposition noted in any CNN poll since the conflict began more than three years ago.

Despite the rising opposition to the war, President Bush said the U.S. will not withdraw from Iraq while he is president.

"In this case, it would give the terrorists and extremists an additional tool besides safe haven, and that is revenues from oil sales," the president said. "Leaving before the job is done would be a disaster," he said. (Full story)

A bare majority (51 percent) say they see Bush as a strong leader, but on most other attributes he gets negative marks. (Interactive: Poll results)

Most Americans (54 percent) don't consider him honest, most (54 percent) don't think he shares their values and most (58 percent) say he does not inspire confidence. (Complete poll results -- PDF)

Bush's stand on the issues is also problematic, with more than half (57 percent) of Americans saying they disagree with him on the issues they care about.

That's an indication that issues, not personal characteristics, are keeping his approval rating well below 50 percent.

Majority disapprove of Bush

Bush's disapproval rating exceeds his approval, 57 percent to 42 percent.

That's in the same ballpark as was found in an August 2-3 poll: Bush garnered a 40 percent approval.

And that was up slightly from a 37 percent approval in a poll carried out June 14-15.

Fewer than half of respondents (44 percent) say they believe Bush is honest and trustworthy; 54 percent do not.

And just 41 percent say they agree with Bush on issues, versus 57 percent who say they disagree.

Americans are about evenly split on whether their commander-in-chief understands complex issues, with 47 percent saying yes, and 51 percent saying no.

Democrats enjoy lead

Bush's tepid ratings do not bode well for his party's odds in the coming congressional elections. Asked which party's candidate they would vote for if the elections were held today, 52 percent of respondents cited the Democratic Party's; 43 percent the GOP's.

Bush dismissed a question about his popularity during a news conference Monday.

"I don't think you've ever heard me say: 'Gosh, I better change positions because the polls say this or that,'" he told reporters. "I've been here long enough to understand, you cannot make good decisions if you're trying to chase a poll."

He added, "I'm going to do what I think is right, and if, you know, if people don't like me for it, that's just the way it is."

The poll of 1,033 Americans was carried out for CNN by Opinion Research from Friday through Sunday.

The polls had sampling errors of plus-or-minus 3 points.