Barrack, the US envoy to Syria and ambassador to Turkey, has recently visited Iraq multiple times to meet with senior officials.

Maliki's media office said in a short statement that the PM candidate stressed during the meeting "the need to respect Iraq's sovereignty and the will of its people".

He also spoke of the "importance of supporting the democratic process and strengthening political stability" in Iraq.

It wasn't clear what message Barrack conveyed to Maliki.

Last month President Donald Trump intervened in Iraq's affairs by issuing an ultimatum that if Maliki -- a two-time former premier with close ties to Iran -- was named Iraq's next prime minister, the US would no longer help the country.

Trump's threat left Iraqi leaders at a loss, particularly within the Coordination Framework -- a ruling alliance of Shiite groups with varying degrees of links to Iran that nominated Maliki.

Earlier this week, Maliki told AFP he would not withdraw his nomination, while also seeking to allay Washington's concerns.

"I have absolutely no intention of withdrawing out of respect for my country, its sovereignty, and its will," Maliki told AFP in an interview.