The remains of ISIS leader Abu Bakr-al Baghdadi was "disposed of appropriately" in accordance with the US standard operating procedure and the law of armed conflict, the chairman of the Joint Chiefs of Staff has said.

US President Donald Trump announced on Sunday that Baghdadi blew himself in his suicide vest as he was chased to the dead end of a tunnel by the US service dogs during an American raid in northwest Syria.

Addressing reporters in the Pentagon, Chairman of the Joint Chiefs of Staff General Mark Milley said, "Baghdadi's remains were transported to a secure facility to confirm his identity with forensic DNA testing and the disposal of his remains has been done. It is complete and was handled appropriately."

"His remains were disposed of appropriately in accordance with our SOP (standard operating procedure) and the law of armed conflict," the top general said.

Al-Qaeda leader Osama bin Laden was buried at sea after being killed in a US raid in Pakistan's Abbottabad in 2011.

Responding to questions, General Milley said the US forces also took with them materials about ISIS and future planning from the compound where Baghdadi was killed.

"There was material taken away. I don't want to characterize exactly what or how much yet until it gets exploited properly. But as a matter of course, we always do sensitive side exploitation on any objective anywhere to do that. As to whether it was Baghdadi's headquarters, it was an area in which he was staying on a consistent basis," the chairman of the Joint Chiefs of Staff said.

He also said that US forces captured two associates of Baghdadi.

"There were two adult males taken off the objective alive and they are in our custody," General Milley said.

Asked about President Trump saying that Baghdad was whimpering and crying before he died, General Milley said the presidential account was based on the conversation that he had with those involved in the attack.

"The (defense) secretary was asked the same question yesterday. I note the president had planned to talk down to the unit and unit members, but I don't know what the source of that was, but I assume it was talking directly to the unit and the unit member," he said.