The U.S. leader stopped short of calling for Nouri al-Maliki to resign, saying “it’s not our job to choose Iraq’s leaders.” But, his carefully worded comments did all but that.

“Only leaders that can govern with an inclusive agenda are going to be able to truly bring the Iraqi people together and help them through this crisis,” Obama declared at the White House.

“We’ve said publicly, that whether he (al-Maliki) is prime minister or any other leader aspires to lead the country, that there has to be an agenda in which Sunni, Shiite and Kurd all feel that they have the opportunity to advance their interest through the political process,” the president said.

An “inclusive agenda” has not been high on the priorities of al-Maliki, whose credibility as an able leader suffered a serious setback when Sunni militants of the al-Qaida-inspired Islamic State of Iraq and the Levant launched a lightning offensive last week that swallowed up a large chunk of northern Iraq, together with the nation’s second city, Mosul.

Al-Maliki, who rose from relative obscurity to office in 2006, when Iraq’s sectarian bloodletting began to spiral out of control, quickly became known for a tough hand, working in alliance with American forces in the country since the 2003 invasion that toppled Saddam Hussein.

Over the years that followed, Sunni tribes backed by the Americans rose up to fight al-Qaida-linked militants, while al-Maliki showed a readiness to rein in Shiite militiamen — and by 2008, the violence had eased.

Since the withdrawal of American forces in late 2011, however, it has swelled again, stoked in part by al-Maliki himself.

The Iraqi leader’s moves last year to crush protests by Sunnis complaining of discrimination under his Shiite-led government sparked a new wave of violence by militants, who took over the city of Fallujah in the western, Sunni-dominated province of Anbar and parts of the provincial capital Ramadi. Iraqi army and police forces battling them for months have been unable to take most areas back.

At the same time, many Iraqis complain of government corruption, the failure to rebuild the economy and too close ties with mostly Shiite Iran, a non-Arab nation that Sunni Arab states, including powerhouse Saudi Arabia, see as a threat to regional stability.

Shiite politicians familiar with the secretive efforts to remove al-Maliki said two names mentioned as possible replacements are former vice president Adel Abdul-Mahdi, a French-educated economist who is also a Shiite, and Ayad Allawi, a secular Shiite who served as Iraq’s first prime minister after Saddam’s ouster.

Al-Mahdi belongs to a moderate Shiite party, the Supreme Islamic Iraqi Council, which has close links with Iran.

Also lobbying for the job is Ahmad Chalabi, a Shiite lawmaker who recently joined the Supreme Council and was once a favorite by Washington to lead Iraq a decade ago. Another Shiite from the Supreme Council who is trying to land the job is Bayan Jabr, a former finance and interior minister under al-Maliki’s tenure, according to the politicians, who spoke on condition of anonymity because of the sensitivity of the subject.