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Two Iraqi groups backed by Iran are demanding all US forces leave Iraq, opposing plans by Baghdad and Washington to retain a training and advisory capacity.
An Iraqi government spokesman said on Monday that US forces had begun reducing their numbers.
The Badr Organisation, a Shiite group that has a minister in Prime Minister Haider Al Abadi's government in charge of the interior, said remaining US troops would cause instability.
"The two governments should co-ordinate to ensure a full withdrawal. US presence will be cause for internal polarisation and a magnet for terrorists," Badr spokesman Kareem Nuri said.
Kataib Hezbollah, a militant, secretive and anti-American group, repeated threats to attack US forces. The US State Department has claimed it has links to its Lebanese namesake.
"We are serious about getting the Americans out, using the force of arms because the Americans don't understand any other language," its spokesman, Jaafar Al Husseini, told Beirut-based Al Mayadeen TV on Monday.
Kataib Hezbollah has strong links to Iran's Revolutionary Guard Corps and has threatened to attack US forces several times, describing their presence as an occupation.
The US-led international military coalition helped Iraqi forces recapture territory taken by ISIL in 2014 and 2015, providing air and artillery support in the battle for Mosul, and trained tens of thousands of elite Iraqi soldiers.
The Pentagon says it has about 5,300 troops in Iraq, although last year an official quoted by Newsweek put the number at 7,000.
"The coalition will tailor our forces in consultation with our Iraqi partners in order to ensure the lasting defeat of Daesh, " the coalition's director of operations, Brig Gen Jonathan Braga, said on Monday.
Gen Braga said that even if the composition of the force changes, the coalition would maintain the capabilities and presence to continue to train, advise and equip Iraqi forces to ensure that ISIL does not re-emerge.
US officials said that while ISIL has lost most of the territory it controlled in Iraq and Syria, there is concern about fighters returning to insurgency tactics.