Baghdad, Iraq (CNN) -- The two most senior leaders of al Qaeda in Iraq have been killed in a joint Iraqi-U.S. operation, officials announced Monday.
The deaths of Abu Ayyub al-Masri and Abu Omar al-Baghdadi deal "a potentially devastating blow" to the terrorist group, the U.S. military said.
"The death of these terrorists is potentially the most significant blow to al Qaeda in Iraq since the beginning of the insurgency," the commander of U.S. Forces-Iraq, Gen. Raymond Odierno, said in a news release.
In an exclusive interview with CNN, Odierno said it would be "very difficult" for the al Qaeda network to replace the two men.
The two were killed in a Sunday morning strike that "broke al Qaeda's backbone," Iraqi Prime Minister Nuri al-Maliki said.
Al-Masri, a native of Egypt, was military leader of al Qaeda in Iraq. Al-Baghdadi was leader of the Islamic State of Iraq, an umbrella group that includes al Qaeda in Iraq. The U.S. military said al-Baghdadi held the title "Prince of the Faithful."
Odierno said al-Masri was the link in Iraq to Osama bin Laden and al Qaeda: "That was the foreign element of al Qaeda that was established here." Al-Masri became the head of al Qaeda in Iraq in 2006 after Abu Musab al-Zarqawi was killed in a U.S. attack.
Al-Masri's assistant and al-Baghdadi's son, who also were involved in terrorist activities, were killed as well, the U.S. military said.
A U.S. soldier was killed during the assault when a U.S. helicopter crashed, the military said in the news release.
Vice President Joe Biden, who has been delegated to take the Obama administration's lead role in Iraq, made a rare appearance at the daily White House briefing on Monday to announce that Iraqi Security Forces killed the "two most senior leaders of Al Qaeda Iraq."
He stressed that Iraqi forces led the operation, saying, "This action demonstrates the improved security, strength and capacity of Iraqi security forces. The Iraqis led this operation, and it was based on intelligence the Iraqi security forces themselves developed."
Al-Maliki said the operation -- in al-Tharthar, about 10 kilometers south of Tikrit -- thwarted a plan by al Qaeda in Iraq to attack churches in Baghdad in the last two days.
The troops found messages between the leaders of al Qaeda in Iraq and top figures in al Qaeda -- including leader Osama bin Laden and his deputy, Ayman al-Zawahiri, said al-Maliki.
An Iraqi intelligence cell pursuing high-level leaders of al Qaeda in Iraq gathered information for the operation, he said.
The two men were hiding in a hole within a house, where their bodies were eventually found by security forces, he said.
The arrests of many other senior leaders of al Qaeda in Iraq in the last couple of days led authorities to discover the safe house, al-Maliki said.
There had been previous reports of al-Baghdadi being killed that turned out to be false. While other people have operated under the same name, authorities are confident the man killed Sunday is Abu Omar al-Baghdadi, al-Maliki said Monday.
Al-Masri was once reported captured, which turned out to be inaccurate.
Security forces arrested 16 "additional suspected criminal associates of the warranted individuals," the military said.
CNN's Jomana Karadsheh, Mohammed Jamjoom and Yousif Bassil contributed to this report.