Iraq has asked the United States to begin the process of planning the withdrawal of its troops from the country, five days after the Iraqi Parliament voted to end the long-standing American military presence there in the wake of the U.S. killing of Iranian Gen. Qassem Soleimani.

Prime Minister Adel Abdul-Mahdi said in a statement Friday that he had asked Secretary of State Mike Pompeo in a phone call "to send a delegation to Iraq to put a mechanism [in place] for implementing the Iraqi parliament decision to safely withdraw troops from Iraq."

This was, he said, because "Iraq is keen to keep the best relations with its neighbors and friends within the international community, and to protect foreign representations and interests and all those present on Iraqi soil."

The prime minister also said the U.S. has been moving troops into the country and operating drones without authorization and contrary to an agreement between the two countries.

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However, later Friday, Pompeo indicated that the troops would remain in the country, saying that the U.S. would continue its mission to help train Iraqi security forces and counter the Islamic State militant group.

"We are happy to continue the conversation with the Iraqis about what the right structure is," Pompeo said at the White House. "Our mission set there is very clear. We've been there to perform a training mission to help the Iraqi security forces be successful and to continue the campaign against ISIS.

"We're going to continue that mission but, as times change and we get to a place where we can deliver upon what I believe and what the president believes is our right structure with fewer resources dedicated to that mission, we will do so."

The U.S. announced it was sending 3,000 more troops to the Middle East last week after thousands of people, some aligned to Iranian-backed militias, protested at the U.S. Embassy in Baghdad and gained access to a reception area.

The presence of U.S. troops in Iraq — a fact of life in the country since the 2003 U.S.-led invasion — has become the source of debate and controversy in recent days.

A leaked letter from the commanding general of U.S. and allied troops in Iraq told the country's Ministry of Defense it would be "re-positioning forces over the course of coming days and weeks to prepare for onward movement."

However, Pentagon chiefs have been quick to stress that there were, in fact, no plans to leave Iraq. The chairman of the Joint Chiefs of Staff, Gen. Mark Milley, has also denied the United States was leaving, describing the memo as "a mistake" and an unsigned draft.

The removal of the 6,000 or so American troops in Iraq would affect Operation Inherent Resolve, the multinational coalition dedicated to fighting ISIS. That coalition stood down from its campaign against the terrorist group after Soleimani's killing to concentrate on defending U.S. bases.

Politicians in the region and terrorism experts have warned that the American decision to step back from the fight against ISIS could provide a boost to extremists and an opportunity for Russia to increase its influence in Iraq.