Maliki called on Sunni tribal groups in restive Anbar province to take the initiative against al-Qaida forces that took control over parts of the restive cities of Fallujah and Ramadi.
Al-Qaida's rise in Anbar province followed protests from members of the Sunni community frustrated Maliki, a Shiite, was sidelining them.
Levin said Thursday he was frustrated with the leadership style of the two-term prime minister.
"It is a tragedy for the Iraqi people, and a real security concern for the United States, that Prime Minister Maliki has yet to produce a strategy for broadly based governance in Iraq," he said in a floor statement.
Levin, however, said that ignored the policies enacted by Obama's predecessor.
"We should not forget that the 2011 withdrawal date for American troops from Iraq was negotiated by President [George W.] Bush," he said.
Levin said a decision to keep U.S. boots on the ground past 2011 was rejected because Iraq didn't want to give legal protection to U.S. combat forces.