Only in the United States did a majority of those questioned, 57 percent, have a positive view of President Bush's role.
The AP polls were conducted by Ipsos, an international polling firm, in Britain, Canada, France, Italy, Germany, Mexico, Spain and the United States.
Just over half in Mexico and Italy had a negative view of Mr. Bush's role. In Britain, the closest U.S. ally in the war in Iraq, and in Canada, two-thirds had a negative view.
Sam McGuire, director of opinion research at Ipsos UK, said Mr. Bush's low ratings in Britain are notable, given that country's close alliance with the United States. Britain traditionally has been seen as the United States' "staunchest European ally on world affairs," he said, and long has been a buffer between the United States and Europe.
Three-fourths of those in Spain and more than 80 percent in France and Germany had a negative view of Mr. Bush's role in world affairs.
"Bush has a lot of work to do if he wants to be popular in France," said Edouard LeCerf, director of opinion research for Ipsos France.
The AP-Ipsos poll found that people in the two countries bordering the U.S. and in five major European countries think the war in Iraq increased the threat of terrorism in the world.
In the United States, people were evenly divided on whether the war has increased or decreased the terror threat.
While a majority in each of the countries polled except the United States said the terrorism threat was greater because of the war, fewer than one in 10 in any of the European countries said the terror threat had been decreased by the war.
In Canada and France, just over half felt it had been increased, while in Germany, three-fourths thought the Iraq war has made the terror problem worse.
A majority in each country, including the United States, said they felt the situation between Israel and the Palestinians has made the terror threat around the world worse.
Overall concern about terrorism was very high in Italy and Germany, where about seven in 10 said they were very worried or somewhat worried, and especially in Spain, 85 percent, where residents also have to contend with domestic terrorism by Basque separatists. The high levels of concern about terrorism are probably linked to the recent history of terror in those countries, one public opinion analyst said.
"Italy and Germany were the countries most heavily affected by terrorism during the 1970s," said Christian Holst, director of opinion research at Ipsos Germany. "This kind of sticks in people's memories — the older they are, the more they remember, and the higher the level of fear is."
Fewer than half in Canada said they were worried about terrorism, a finding that didn't surprise Darrell Bricker, president of public affairs polling of Ipsos-Reid in Canada.
"Our experience with terrorism tends to be on the news and south of the border, not here," Bricker said.
People in the different countries had a more mixed reaction about whether Britain and the United States should have gone to war in Iraq, if it turns out no weapons of mass destruction are found.
Of the eight countries polled, a majority in five countries — the United States, Canada, Mexico, Italy and Britain — said that even if no weapons of mass destruction are found in Iraq, there were other reasons to justify the war.
The AP-Ipsos polls of 930 to just over 1,000 adults in each country were taken Feb. 12-21, and have margins of sampling error of plus or minus 3 percentage points.