Two major Iraqi Shia groups backed by Iran are demanding all U.S. forces leave Iraq, opposing plans by Baghdad and Washington to keep some there for training and advisory purposes.
An Iraqi government spokesman said on Monday U.S. forces - who number more than 5,000 - had begun reducing their numbers but some would remain.
The Badr Organization, a Shia group that has a minister in Prime Minister Haider al-Abadi's government, in charge of the interior, said any remaining U.S, troops would be cause for instability.
"The two governments should coordinate to ensure a full withdrawal. U.S. presence will be cause for internal polarization and a magnet for terrorists," Badr spokesman Kareem Nuri said.
Kataib Hezbollah, a more militant, secretive and anti-American group, repeated threats to attack U.S forces.
"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 evening.
Kataib Hezbollah has strong links to Iran's Revolutionary Guards Corps and has threatened to attack U.S. forces several times in the past, describing their presence as an occupation.
A U.S. official in Baghdad said: "We take anything that sounds like a threat from anyone against Americans seriously."
"There's not that many of us here and we are all operating within Iraqi military bases. A lot of this is frankly just political posturing and trying to take advantage of stories in the press to make broader political points," he added.
The U.S.-led international military coalition helped Iraqi forces recapture territory taken by Islamic State in 2014 and 2015, providing air and artillery support in the battle to for Mosul, and trained tens of thousands of elite Iraqi soldiers.
"The Coalition will tailor our forces in consultation with our Iraqi partners in order to ensure the lasting defeat of Daesh (Islamic State)," the coalition's director of operations, Brigadier General Jonathan Braga, said in a statement on Monday.
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 Islamic State does not re-emerge.
U.S. officials say that while Islamic State has lost most of the territory it once controlled in Iraq and Syria, there is concern about surviving fighters returning to insurgency tactics.