Al-Masri took over the leadership of al-Qaeda in Iraq after its leader Abu Musab al-Zarqawi was killed in a US airstrike last June in Diyala province northeast of Baghdad.
Iraq has meanwhile closed its borders with Iran and Syria as part of Operation Law and Order, said to be aimed at stopping foreign fighters and weapons entering the country.
Iraqi and British forces closed two crossings on Thursday, expanded coastal patrols and increased checkpoints in Basra.
Iraq had said it would shut the borders for 72 hours.
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The US military said: "The plan to close the borders went into effect last night. Many points were closed, but I can't confirm that all were shut."
A British military spokesman said border crossings in Basra and Maysan provinces had been sealed by British and Iraqi forces.
Meanwhile, Moqtada al-Sadr, the Iraqi Shia leader, is said to have been spotted in the southern Iraqi town of Kufa, Al Jazeera reports.
Until now, his whereabouts were unclear, with some sources in the US saying that he had fled to Iran.
Al-Sadr's aides denied reports he had left to avoid an offensive against his Mahdi Army militia.
However, Iraq's president said he believed al-Sadr had asked some members of his Mehdi army to leave Iraq to "make the Baghdad security plan easier".
Jalal Talibani also told a news conference in Baghdad that he was unaware of al-Sadr's whereabouts.
Even as the plan for Baghdad gathered steam, a suicide car bomber struck in Ramadi, in Anbar province, killing at least 11 people including four policemen, AFP quoted the US military as saying.
Al Jazeera's correspondent in Baghdad said three car bombs killed four people and wounded 20 in the predominantly Sunni Doura district.
A bomb inside a bus in the predominantly Shia Sadr City killed two people and wounded five others, an interior ministry source said.
Another six people, including three policemen, were killed near Baquba, northeast of Baghdad, a police officer said.
Also in Baghdad, a car bomb targeting an Iraqi army patrol wounded a soldier.
Iraqi police said a roadside bomb killed two people and wounded a third when it exploded next to their car near the the city of Kirkuk, 250km north of the capital.
Earlier, another roadside bomb hit a police patrol, killing a policeman in the northern city of Mosul.
US-Iraqi forces sealed off six districts of Baghdad, following several early-morning raids.
A US marine was killed in combat operations in Anbar, the US military said on Thursday.
The soldier, assigned to the Multi-National Force-West, was killed on Wednesday during fighting in an area considered one of the Sunni fighters' strongholds.