It answers to Iraq 's prime minister as commander-in-chief of the Iraqi armed forces, into which it has been integrated by a parliamentary vote.
The global battle against the militant Islamic State group in northern Iraq since 2014 saw the United States and Iran effectively fighting on the same side, with both supporting the Iraqi government against the militants.
The PMF is comprised of dozens of organizations, including Sunni Muslim, Yazidi, Christian and Shiite Turkmen groups. Shi'ites form a plurality among Iraqis.
"Mr Tillerson is expected tonight in Baghdad to meet Mr Abadi, who has returned from visits to Riyadh, Cairo and Amman", the official said.
Al-Abadi appeared to have rebuffed Tillerson's call to disband Iran-backed militias during their meeting in Baghdad on Monday.
U.S. Secretary of State Rex Tillerson smiles alongside Qatar's Foreign Minister Sheikh Mohammed bin Abdulrahman Al Thani during a media availability after their meeting, in Doha, Qatar October 22, 2017.
"Your forces should get ready to get out of our country once the excuse of Daesh's presence is over", said Asaib's leader, Qais al-Khazali, according to the group's TV channel, al-Aahd.
Iraq on Monday rebuffed a USA demand that Iranian militias leave the country, insisting that the paramilitary forces which helped it defeat the Islamic State group consist exclusively of Iraqi nationals. The council's creation was promoted by the Trump administration to improve relations between Saudi Arabia, Iran's main regional rival, and Iraq, whose majority Shi'ite-dominated government has close ties with Tehran.
"Exactly what country is it that Iraqis who rose up to defend their homes against ISIS return to?", Zarif said in a tweet.
The Iraqi government strongly opposed the referendum vote and sent troops last week into several Kurdish-held territories to seize back control for the central government.
"We are concerned and a bit sad", Tillerson said.
"We have friends both in Baghdad and in Irbil, and we encourage both parties to enter into discussion and dialogue", he said.