"We may take certain parts of it and release it," Trump said on departure from Washington to Chicago, where he was due to address a police officers' convention.

The attack by US special forces deep into 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.

Trump described the raid in unusually colorful and detailed terms on Sunday, saying that Baghdadi died when he exploded 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.