BAGHDAD — Prime Minister Nuri Kamal al-Maliki announced Monday that two top insurgent leaders had been killed, including a somewhat mythic figure who has operated under the name Abu Omar al-Baghdadi. Mr. Baghdadi has been reported dead or detained several times previously, and his very existence had been called into question a few years ago by American military leaders.

After Mr. Maliki’s press conference, the American military released a statement verifying that Mr. Baghdadi was killed in a joint raid between Iraqi and United States forces in the dark hours of Sunday morning near Tikrit, near Saddam Hussein’s hometown.

Also killed, according to Mr. Maliki and American officials, was Abu Ayyub al-Masri, the leader of Al Qaeda in Iraq, also known as Al Qaeda in Mesopotamia, a largely Iraqi group that includes some foreign leadership.

Both men were found in a hole in the ground.

“The security forces surrounded the hole, and when they got them out they were dead,” Mr. Maliki said at the news conference. Mr. Maliki said computers and letters were found that included communication between the men and Osama bin Laden.