The US President says he's considering releasing footage of the raid in which the leader of Islamic State was killed at the weekend.
Abu Bakr al-Baghdadi is said to have blown himself up after being cornered by American forces during a raid in Syria.
Speaking to reporters earlier, Mr Trump said the US had "captured a man that should’ve been caught a long time ago".
In response to a specific question about video of the operation, he responded: "The question was: Am I considering releasing video footage of the raid?
"And we may take certain parts of it and release it, yes."
It comes as a number of media reports questioned the US president's detailed account of the raid.
Mr Trump yesterday suggested al-Baghdadi "died after running into a dead-end tunnel... whimpering and crying and screaming all the way".
He claimed watching footage of the raid from the White House situation room was like "watching a movie".
Officials told the New York Times that the president had seen "overhead surveillance footage on several video screens that, together, provided various angles from above, and in real time".
The report suggests that any more specific details such as 'whimpering' would have had to be communicated to the US president by military commanders.
al-Baghdadi, who had a US$25m (€22.5m) bounty on his head, had been the subject of an international manhunt for years.
He was known to be at the location of the operation 48 hours prior to the attack, a senior Turkish official said.
No US personnel are believed to have been killed in the operation targeting the IS leader, but President Trump said a "large number of al-Baghdadi’s fighters and companions were killed with him".