Mahdi made the request in a telephone call with Pompeo on Thursday, the Post said.
The strikes were in retaliation for the U.S. drone strike that killed Revolutionary Guard General Qassem Soleimani, the country's most powerful commander, in Baghdad last week.
Military bases in Iraq hosting USA troops have been targeted by rocket and mortar attacks from Iran-backed militias in recent months.
Moreover, the public posturing on the matter points to the tensions that remain in the wake of the United States killing of a top Iranian military commander on Iraqi soil last week and the uncertain road ahead for the Trump administration's approach to relations with Iraq.
The AP report said that U.S. Secretary of State Mike Pompeo asserted, in reply, "Our mission set there is very clear".
The prime minister also said the US has been moving troops into the country and operating drones without authorization and contrary to an agreement between the two countries.
This came after President Trump on Thursday called for more North Atlantic Treaty Organisation involvement in the Middle East.
The State Department on Friday rebuffed the Iraqi government's request to begin discussions on pulling out troops, saying that any American officials going to Baghdad during a state of heightened tensions would not discuss a "troop withdrawal", as the Iraqi prime minister had requested.
"However, there is a need for a conversation between the governments of the United States and Iraq not only regarding security, but also about our financial, economic and diplomatic partnership", spokeswoman Morgan Ortagus said in a statement.
Ortagus did not elaborate. Sunni and Kurdish lawmakers oppose the Parliament resolution.
No group immediately claimed responsibility.
But the rallies were met with violence, with almost 460 people killed and more than 25,000 wounded since they began.
"Screw Iran! Screw America!" protesters chanted in the capital's Tahrir Square, the epicentre of the anti-regime movement.
Abdul-Mahdi resigned past year, but he has continued to preside over the government in an acting capacity.
An adviser to the prime minister, Abd al-Hassanein al-Hanein, said that while the threat of sanctions was a concern, he did not expect the U.S.to go through with it.
"Everyone is required to think carefully about what this situation will lead to if there is no end to it", he added.