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.

One United States soldier died during the operation in a helicopter crash, which officials said was not caused by enemy fire.

“The death of these terrorists is potentially the most significant blow to Al Qaeda in Iraq since the beginning of the insurgency,” said Gen. Ray Odierno, the top American military commander in Iraq, in a statement. “The Government of Iraq intelligence services and security forces supported by U.S. intelligence and special operations forces have over the last several months continued to degrade A.Q.I. There is still work to do but this is a significant step forward in ridding Iraq of terrorists.”

The American military said Mr. Masri had replaced the former leader of Al Qaeda in Mesopotamia, Abu Musab al-Zarqawi, who was killed in 2006. The American military described Mr. Masri as being “directly responsible for high profile bombings and attacks against the people of Iraq.”

While violence is down dramatically in Iraq compared to the worst days of the insurgency and sectarian violence in 2006 and 2007, the country still faces daily attacks in the form of car bombs, improvised explosive devices and assassinations.

The Sunni insurgency, whose face was Al Qaeda in Mesopotamia, deteriorated in recent years after American forces persuaded groups of fighters to switch sides by paying them cash and promising them jobs, a movement that became known as the Awakening.