"We may take certain parts of it and release it," Trump told reporters.

The operation by US special forces in Syria took place Saturday, culminating in the death of the fugitive leader who at his peak headed an organization that attempted to set up a hardline Islamic state across a huge area of Iraq and Syria.

Addressing a Pentagon briefing, the chairman of the Joint Chiefs of Staff, General Mark Milley, said the footage of Baghdadi's last moments was still being vetted.

"We do have video, photos. We're not prepared at this time to release those. They're going through a declassification process," Milley said. He indicated that some imagery of the operation could be publicly released once declassified.

Trump described the raid in unusually colorful and detailed terms on Sunday, saying that Baghdadi died when he detonated a suicide vest after being cornered by US soldiers in a tunnel, together with three children.

He died "like a dog," Trump said in his comments, which differed sharply in tone from similar announcements by presidents in the past.

A report in The New York Times, quoting military and intelligence officials, cast doubt on some of Trump's descriptions, including his repeated claim that Baghdadi was "whimpering and crying" in the tunnel.

Trump said his account was based on having watched the whole raid in real time, like "a movie."

According to the report, Trump would not have had access to audio of the events at the time, or have been able to see footage from inside the tunnel.

Milley said he could not confirm the details in Trump's account, but that the president "had planned" to talk directly to the troops involved.

"I don't know what the source of that was. But I assume it was talking directly to the unit members," Milley said.