In the strongest sign yet of U.S. doubts about Iraq's stability, the Obama administration is weighing whether to press the Shiite prime minister to step down in a last-ditch effort to prevent disgruntled Sunnis from igniting a civil war.
An Iraqi Shiite lawmaker, Shiite Hakim al-Zamili, said he was aware of a meeting in recent days between Iraqi political leaders and U.S. officials over the issue of al-Maliki's future. He said he did not know who attended the meeting.
Al-Zamili belongs to a political bloc loyal to anti-U.S. cleric Muqtada al-Sadr, who has publicly demanded that al-Maliki, in office since 2008, be replaced.
"My view is that safeguarding Iraq is now our top priority," al-Zamili said, referring to the loss of a vast chunk of northern Iraq to the militants over the past week. "We will settle the accounts later."
Mohammed al-Khaldi, a top aide to outgoing Sunni speaker of parliament, Osama al-Nujaifi, said: "We have asked the Americans, Britain, Turkey, Saudi Arabia and Iran to work toward denying al-Maliki a new term. The Shiite bloc must find a replacement for him."
Besides the Sunnis, many of al-Maliki's former Kurdish and Shiite allies have been clamoring to deny the prime minister a third term in office, charging that he has excluded them from a narrow decision-making circle of close confidants.
"We wanted him to go but after what happened last week we want it even more," said Mahmoud Othman, a veteran Kurdish politician.
Al-Maliki said this week that the newly elected parliament will meet within days to elect a new president who will in turn ask the leader of the chamber's largest bloc to form a new government. His State of the Law bloc won 92 of the chamber's 328 seats in the April 30 election. He needs a majority of at least 165 lawmakers.
It took al-Maliki several months after the 2010 parliamentary elections to cobble together a government.
The prime minister, who has long faced criticism for not making his government more inclusive, has been adopting conciliatory language in recent days toward Sunnis and Kurds. He said the militant threat affects all Iraqis regardless of their ethnic or religious affiliation and called on Iraqis to drop all "Sunnis and Shiites" talk.
Al-Maliki also made a show of meeting Tuesday with Shiite, Sunni and Kurdish political leaders. A statement issued after the meeting said they agreed to set aside differences and focus on "national priorities."
Despite the warm words, al-Maliki is not known to have made any concrete offers to bridge differences with the Sunnis or the Kurds, who have been at loggerheads with the prime minister over their right to independently export oil from their self-rule region in the north and over territorial claims.
The Beiji oil refinery, where Iraqi forces were battling ISIL militants, lies some 250 kilometers (155 mile) north of Baghdad.
A witness who drove past the facility said the militants manned checkpoints around it and hung their black banners on watchtowers. He spoke on condition of anonymity because he feared reprisals.
One of the militants laying siege to the refinery confirmed by telephone that the facility remained in government hands, saying helicopter gunships slowed the insurgents' advance. The militant identified himself only by his alias, Abu Anas, and there was no way to verify his identity or location.