US Defence Secretary Mark Esper has denied US troops are pulling out of Iraq, after a letter from a US general there suggested a withdrawal.
The letter said the US would be "repositioning forces in the coming days and weeks" after Iraqi MPs had called for them to leave.
Mr Esper said there had been "no decision whatsoever to leave".
The confusion came amid threats to American forces after the US killed top Iranian commander Qasem Soleimani.
He died in a US drone strike in Baghdad on Friday on the orders of Mr Trump.
The killing has sharply increased regional tensions, with Iran threatening "severe revenge".
What was in the letter?
It appeared to have been sent by Brig Gen William H Seely, head of the US military's task force in Iraq, to Abdul Amir, the deputy director of Combined Joint Operations.
It starts: "Sir, in due deference to the sovereignty of the Republic of Iraq, and as requested by the Iraqi Parliament, and the Prime Minister, CJTF-OIR (Combined Joint Task Force - Operation Inherent Resolve) will be repositioning forces over the course of the coming days and weeks to prepare for onward movement."
This coalition memo appears to be genuine - but also misleading and badly phrased. Am told by coalition source that it’s to let #Iraq know that US is moving troops out of Green Zone to provide Force Protection elsewhere. NOT leaving #Iraq pic.twitter.com/Erpid6ct6E— Jonathan Beale (@bealejonathan) January 6, 2020
The letter says certain measures, including increased air traffic, will be conducted "during hours of darkness" to "ensure the movement out of Iraq is conducted in a safe and efficient manner".
It would also "alleviate any perception that we may be bringing more Coalition Forces into the IZ (Green Zone in Baghdad)".
How has it been explained?
Mr Esper told reporters in Washington: "There's been no decision whatsoever to leave Iraq. I don't know what that letter is... We're trying to find out where that's coming from."
The highest-ranking US soldier, Chairman of the Joint Chiefs of Staff Mark Milley, then appeared at a briefing, saying the letter was "a mistake".
He said it was a draft which was poorly worded, had not been signed and should not have been released. It was being circulated for input, including from Iraqis.
"[The letter] was sent over to some key Iraqi military guys in order to get things co-ordinated for air movements, etc. Then it went from that guy's hands to another guy's hands and then it went to your hands. Now it's a kerfuffle."
Gen Milley reiterated that US troops were not leaving.
So what is happening?
Gen Milley said the issue was being "worked" with the Iraqis, but gave no details.
BBC defence correspondent Jonathan Beale said he had been told by a coalition source that the letter was to let the Iraqis know the US was moving troops out of the Green Zone to provide protection elsewhere and did not mean a withdrawal.
This has been backed up by other coalition sources, telling separate reporters that the move was to "thin out" the Baghdad personnel.
Why are US troops in Iraq?
In 2003, US-led forces invaded Iraq to overthrow President Saddam Hussein and eliminate weapons of mass destruction that turned out to not to exist.
President George W Bush promised a "free and peaceful Iraq", but the country was engulfed by a sectarian insurgency that cost tens of thousands of lives.
US combat troops withdrew in 2011 after Washington and Baghdad failed to negotiate a new agreement governing their status.
In 2014, when the Islamic State (IS) group seized control of large parts of Iraq, US forces returned at the invitation of the Iraqi government as part of an international coalition tasked with training and advising the Iraqi security forces.
The Baghdad government declared the military defeat of IS at the end of 2017, but about 5,000 US personnel remained to help local forces prevent a jihadist resurgence. Despite continuing IS attacks, some Iraqi political groups - many of them linked to Iran - began calling on the US troops to leave.
Outgoing Iraqi Prime Minister Adel Abdul Mahdi called the US strike that killed Qasem Soleimani a "clear breach of the terms of the American forces' presence".
Days later, the Iraqi parliament approved a non-binding bill urging the government to "cancel the request for help it presented to the international coalition". The bill was backed by most Shia Arab MPs, who hold a majority of seats. Almost 150 Sunni Arab and Kurdish MPs abstained.
It was not immediately clear whether Mr Abdul Mahdi's caretaker administration had the legal authority to end the US military presence.