“I don’t know if there’s anyone in the United States who he listens to anymore,” said Steven Cook, a senior fellow at the Council on Foreign Relations, referring to the embattled prime minister. “Everyone admits that the Iranians have more leverage than the United States.”

While Washington could threaten to call back the roughly 800 U.S. military advisers in the country and withhold future weapons sales to Iraq, such moves would make it even harder for Baghdad to retake the territory it has lost to militants from the Islamic State or prevent them from advancing further north. As long as the Islamic State remains a threat, Cook said Washington will be reluctant to withdraw military support from Iraq despite its anger at Maliki.

The White House is “not ready just yet to punish ourselves by punishing the Iraqis,” he said.

Douglas Ollivant, who formerly served as the top Iraq policy official on the National Security Council, said there was “very little” the United States could do to push Maliki out of power, but he said he didn’t think the Iraqi leader would resort to violence to stay in office.