WASHINGTON (CNN) -- Support for President Bush's management of the war in Iraq has dropped to a new low as he ponders a change in the U.S. strategy there, according to a CNN poll released Monday.

The survey, conducted for CNN by Opinion Research Corporation, found Bush's overall job approval at 36 percent -- little changed from the last CNN poll, taken Dec. 5-7. Sixty-two percent said they disapproved of his performance in office, up from 57 percent in the previous poll.

But support for his management of the war in Iraq dropped considerably, from 34 percent earlier this month to 28 percent in Monday's poll. And a record 70 percent said they disapproved of his handling of the nearly 4-year-old war.

The current poll surveyed 1,019 adults from Friday through Sunday. It has a sampling error of 3 percentage points.

Monday's poll results suggest the widespread dissatisfaction with the Iraq war may be dragging down public approval of Bush's handling of anti-terrorism efforts as well. Support for his management of that issue plunged to 42 percent, down from 50 percent in a poll taken Oct. 13-15, while the percentage of those who disapproved rose from 47 percent to 55 percent -- the first time more than 50 percent have registered disapproval on that topic.

Full poll results