A senior administration official said a severe but unspecified threat against the embassy was the reason that Mr. Trump made the decision to kill General Suleimani.

Yet no major attack against the sprawling and heavily-fortified diplomatic compound in Baghdad’s Green Zone is “imminent,” even though Mr. Pompeo has asserted that repeatedly, said the official, who discussed administration deliberations only on the condition of anonymity. Some Pentagon officials had said earlier that there was no intelligence revealing any unusual threats.

On Tuesday, Mr. Pompeo did not repeat his assertions that the United States had intelligence about an “imminent” attack and instead pointed to recent violent episodes.

“If you’re looking for imminence, you need look no further than the days that led up to the strike that was taken against Suleimani,” Mr. Pompeo said, apparently referring to the rocket attack by an Iranian-backed militia that killed an American interpreter, Nawres Hamid, in Iraq on Dec. 27. The Americans then carried out airstrikes that killed 25 militiamen, which led to protests by mostly Iranian-backed militiamen inside the American Embassy compound in Baghdad.

American officials say that over the last two months, there have been 11 attacks by Iran-backed militias on bases in Iraq where American service members, diplomats and contractors work.

Critics say Mr. Pompeo, the only surviving member of the president’s original foreign policy team, is a chief architect of the rising tensions between the United States and Iran.

As Mr. Trump’s first C.I.A. director, he created a special center to deal with Iran, appointing as its head Michael D’Andrea, a veteran officer and convert to Islam known as the Dark Prince, who oversaw the hunt for Osama bin Laden and the drone strike campaign in the Middle East and Central Asia.