The US military confirmed the deaths of the two men.
"The death of these two terrorists is a potentially devastating blow to al Qaeda in Iraq," the US forces in Iraq said in a statement.
The Iraqi government has previously claimed to have captured or killed Baghdadi on several occasions and the US military has even questioned whether he is an actual person or a fabricated figurehead.
"If it proves true this time, it would be a big blow to al-Qaeda; especially as the [Iraqi] government has been blaming al-Qaeda for the spate of bombing attacks that have been rocking Baghdad over recent weeks," Al Jazeera's Zeina Khodr, reporting from Baghdad, said.
"This event is going to boost the reputation of al-Maliki and the Iraqi security forces, which launched several attacks on al-Qaeda hideouts according to the government.
"The government said the computers they seized in those hideouts showed there were communications between al-Masri and al-Baghdadi. It also showed communication with al-Qaeda's overseas leaders including Osama bin Laden."
Baghdadi was last claimed to have been killed last April, but the Islamic State of Iraq denied the claim and said he was "fine", the SITE Intelligence Group said, according a statement released on internet forums on May 11, 2009.
The timing of the latest operation is vital for al-Maliki who is trying to negotiate support for his State of Law coalition following parliamentary elections in which it emerged as the second largest bloc.