WASHINGTON (Reuters) - A U.S. F-16 warplane that mistakenly dropped a 500-pound bomb on Canadian troops in Afghanistan on Thursday, killing four and wounding eight soldiers, struck after American jets thought they had been fired at from the ground, a U.S. defense official said.

Stressing that reports from the desert training area near Kandahar were "very, very preliminary," the official told Reuters that at least one pilot of a flight of U.S. Air Force F-16s thought the planes had been shot at.

The defense official, who asked not to be identified, said the pilot of the F-16 plane that dropped the laser-guided bomb in the "friendly fire" accident apparently received permission to do so before launching the strike.

But Canada's top military officer said in Ottawa the troops were in a designated training area conducting live fire exercises and the tragedy was "a mystery to us."

President Bush telephoned Canadian Prime Minister Jean Chretien to convey condolences. Defense Secretary Donald Rumsfeld spoke with Canadian counterpart Art Eggleton on the telephone and issued a statement.

"On behalf of the Department of Defense, I want to express my deep regret and sadness over the tragic accident in Afghanistan that killed and wounded a number of Canadian troops," Rumsfeld said. "Our thoughts and prayers go out to them, their comrades and their families."

The secretary said he assured Eggleton that Army Gen. Tommy Franks, head of the U.S. Central Command with responsibility for the war in Afghanistan, would work closely with Canadian military representatives to investigate the accident.

ONE OF WORST 'FRIENDLY FIRE' ATTACKS

It was one of the worst friendly fire accidents of the 6-month war in Afghanistan in which U.S. and allied troops have been hunting al Qaeda guerrillas and fighters of the country's deposed Taliban leadership.

Three U.S. troops and five Afghan fighters were killed and nearly 40 American and Afghan troops injured on Dec. 5 when U.S. B-52 bombers accidentally bombed American special forces troops and supporting Afghan forces north of Kandahar.

"It is just a terrible tragedy," Pentagon spokeswoman Victoria Clarke told Reuters. "The Canadians have been fabulous in their support in the war on terrorism."

Clarke declined to comment on details of the incident, which occurred at 5:25 p.m. Washington time (2125GMT) on Wednesday and shortly before 2 a.m. Thursday in Afghanistan.

The deaths were the first Canadian casualties in the U.S.-led war in Afghanistan and the first casualties Canada has suffered in offensive combat operations since the 1950-53 Korean War. They came just three days after the most recent U.S. casualties in Afghanistan.

In Ottawa, Chretien promised a thorough investigation.

"President Bush called me tonight to offer the sincerest condolences of the American people to the Canadian families. He also pledged complete cooperation with Canadian authorities, who will carry out a thorough and complete investigation," Chretien said.

Canadian Gen. Ray Henault said the U.S. plane clearly misidentified the Canadian forces, who were conducting a live-fire training exercise in the dark in a recognized training zone south of Kandahar.

"My understanding is that there was no hostile activity in the area that would have created this incident," the chief of Canada's defense staff added at a midnight news conference in Ottawa. "How this sort of thing could happen is a mystery to us."

"We remain committed in our duty to this campaign and will certainly continue," said Henault.