WASHINGTON—Iraqi Prime Minister Nouri al-Maliki headed back to Baghdad after a strained visit to Washington that fell short of securing more U.S. military aid and exposed divisions about the causes and cures for rising violence in his country. Mr. Maliki wrapped up his three-day visit Friday with a White House meeting at which President Barack Obama praised the Iraqi leader and said the two countries would step up their efforts to uproot al Qaeda militants expanding their operations across the region. But while Mr. Maliki worked to persuade American leaders to free up more U.S. military aid, leading lawmakers expressed dismay over the Iraqi leader’s repeated insistence that he bore little responsibility for the sectarian violence sweeping his country. Sen. Robert Menendez (D-N.J.), chairman of the Senate Foreign Relations Committee, said he was “extremely disappointed” by his meeting with Mr. Maliki and said the prime minister hurt his case […]