"I believe it probably would've been four embassies," Trump told Fox interviewer Laura Ingraham.
No other officials have backed up the assertion from Trump, who frequently fabricates details to embroider his accounts of events. Congressional Democrats said no such intelligence was relayed to them in briefings last week.
Esper and O'Brien, in a series of television appearances, refused to directly repeat the president's assertion, although they tried to avoid directly contradicting him.
"I didn't see" any specific intelligence regarding attacks on four embassies, Esper conceded, but he declared that "I share the president's view" that the diplomatic posts were "probably" a target.
O'Brien took a similar stance, telling NBC's "Meet the Press" the intelligence showed "they were looking at U.S. embassies throughout the region."
But he declined to detail imminent threats against any diplomatic installation other than the American Embassy in Baghdad, whose gates were breached on New Year's Eve by protesters aligned with a pro-Iranian militia.
"I'd love to have the intelligence out there," O'Brien said. "Unfortunately, if we declassify it, we could end up losing that stream of intelligence."
The episode was reminiscent of Trump aides' efforts last week to dismiss or minimize the president's threat to strike Iranian cultural sites -- an action that would likely have constituted a war crime -- even as the president himself amplified his original remarks.
Trump finally backed down, saying that "I like to obey the law," and there's been no evidence that any Iranian cultural sites were targeted.
Frustrated Democrats said they were well aware of the need to avoid disclosing sources and methods for intelligence reports, but accused the administration of providing an incomplete or outright misleading picture of the factors that allegedly made it imperative to kill Soleimani as a matter of self-defense.
"In the classified briefing, we got less detailed information than President Trump shared with Laura Ingraham," said Sen. Chris Coons of Delaware, interviewed on "Fox News Sunday." That assertion was echoed by Rep. Adam B. Schiff (D-Burbank), the head of the House Intelligence Committee.
On CBS' "Face the Nation," Schiff said there was "no discussion" in briefings with the so-called "Gang of Eight" -- the chairs and ranking members of relevant House and Senate committees and the House and Senate leaders -- of four embassies being targeted. He accused Trump and Secretary of State Michael R. Pompeo of "fudging the intelligence" in public comments about the Soleimani strike.
The administration, Schiff said, is "overstating and exaggerating what the intelligence shows. And when you're talking about justifying acts that might bring us into warfare with Iran, that's a dangerous thing to do."
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