Asked on CBS’s Face the Nation if there had been a specific or tangible threat, Esper said: “I didn’t see one with regard to four embassies.”

Trump’s claim on Fox News on Friday prompted fierce criticism from members of Congress who were not briefed before the strike and who say such a threat was not mentioned in a classified briefing on Wednesday.

On Sunday, Esper added: “What I’m saying is I share the president’s view that, probably, my expectation was that they were going to go after our embassies.

“We had information that there was going to be an attack within a matter of days that would be broad in scale, in other words more than one country, and that it would be bigger than previous attacks, likely going to take us into open hostilities with Iran.

“We had every expectation to believe this would happen. That threat has been disrupted.”

Suleimani was killed by a drone strike at Baghdad airport on 2 January. Iran responded with missile strikes on US bases in Iraq. It has also admitted accidentally shooting down a Ukrainian airliner over Tehran, killing 176 people.

Esper later appeared to row back, telling CNN’s State of the Union “what the president said with regard to the four embassies is what I believe as well”.

“There was intelligence that there was an intent to target the US embassy in Baghdad,” he said.

However, Esper’s insistence that such “exquisite intelligence” was shared with the bipartisan Gang of Eight congressional leaders in a briefing was immediately dismissed by Adam Schiff, Democratic chair of the House intelligence committee.

“He’s just plain wrong,” Schiff told CBS. “There was no discussion that, ‘These are the four embassies that are being targeted and we have exquisite intelligence that shows these or those are specific targets.’

“[And] I don’t recall there being a specific discussion about bombing the US embassy in Baghdad. The briefing was more along the lines of what Secretary [of State Mike] Pompeo admitted the other day, that, ‘We don’t know precisely where and we don’t know precisely when.’

“That’s not an intelligence conclusion. That’s Pompeo’s personal opinion.”

Schiff also had harsh words for Trump.

“When you hear the president out there on Fox,” he said, “he’s fudging the intelligence.”

Trump has also mentioned the threat to the Baghdad embassy as a motivation for the strike on Suleimani, but congressional criticism of his attempts to justify precipitating a crisis with Iran remains.

After the classified briefing on Wednesday, Senator Mike Lee of Utah voiced rare Republican criticism of the president.

“I didn’t hear anything about [the four embassies claim],” Lee told CNN on Sunday, appearing to back up Schiff’s assertion. “And several of my colleagues have said the same so that was news to me. It certainly wasn’t something I recall being mentioned at the classified briefing.”

Pompeo has claimed Congress was briefed fully on the rationale for the strike on Suleimani, “the most perilous chapter so far in Trump’s three years in office”, according to a detailed chronology of the crisis published by the New York Times on Saturday.

“I’m sure there was a mention of at least one embassy in that briefing,” Lee said, “because there had been an attack on one of our embassies [in Baghdad, by pro-Iranian militia] leading up to the strike on Suleimani.”

Asked if he agreed with the former Republican now independent congressman Justin Amash, that Trump was guilty of an abuse of his power in ordering the strike without informing Congress, Lee said he did not “doubt there was an imminent attack but it’s frustrating not to get the details of the intelligence behind it”.

The Kentucky senator Rand Paul was more blunt than his fellow Republican on NBC’s Meet the Press, claiming Pompeo had given “contradictory information”.

“We’ve heard from the secretary of state that they don’t know where or when, but it was imminent,” Paul said. “He thinks he can square the circle but to me it seems pretty inconsistent.”

Robert O’Brien, Trump’s national security adviser, parroted the “exquisite intelligence” talking point.

“We had exquisite intelligence to show they were looking at US facilities throughout the region and they wanted to inflict casualties on American soldiers, sailors, airmen, marines, as well as diplomats,” he told NBC.

“The threat was imminent, I saw the evidence,” O’Brien added, declining to elaborate because he said the information was classified. Pressed on his definition of imminent, he said: “Soon, quickly.”

On ABC’s This Week, Democratic House speaker Nancy Pelosi accepted Iran had malignant intentions towards the US but questioned the president’s handling of the crisis.

“A lot of bad actors are doing bad things and threatening bad things to us, we know that,” she said, “Iran being one of them and its proxies doing bad things to our interests and the world.

“But how do we deal with that in a way that calms rather than escalates?”

Trump, meanwhile, continued to seek to capitalise on protests in Iran which broke out after the regime admitted shooting down the airliner.

“To the leaders of Iran,” the president tweeted, “DO NOT KILL YOUR PROTESTERS. Thousands have already been killed or imprisoned by you, and the World is watching. More importantly, the USA is watching. Turn your internet back on and let reporters roam free! Stop the killing of your great Iranian people!”