Secretary of State Mike Pompeo delivered the warning in recent calls to Iraqi President Barham Salih and Iraqi Prime Minister Mustafa al-Kadhimi, the officials said.

U.S. ambassador to Iraq, Matthew Tueller, told Iraq’s Foreign Minister Fuad Hussein that the policy decision had been directed by President Trump and that the two countries had entered a new era in their relations, they added.

The State Department and the U.S. Embassy declined to comment on the diplomatic discussions. Two Iraqi officials said, however, that the U.S. has informed Iraqi authorities that it is beginning to take preliminary steps so it could close the embassy over the next few months while retaining its consulate in Erbil, the capital of the Kurdish region of Iraq.

“What we’re being told is that it is a gradual closure of the embassy over two to three months,” said one Iraqi official, who added that it might be coupled with the withdrawal of American troops in the country. Such a gradual withdrawal would give Washington time to reverse the move should Iraqi authorities take decisive action to protect U.S. facilities, the Iraqi official added, despite the risks of inflaming tensions with Iran and the Iraqi militias backed by the Islamic Republic.

An expanded version of this report appears in WSJ.com.

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