"We mourn you... commander of the faithful," an audio statement read by Abu Hamza al-Quraishi, presented as the jihadist group's spokesman, said.

Baghdadi, who led IS since 2014 and was the world's most wanted man, was killed in a US special forces raid in Syria's northwestern province of Idlib on Sunday.

The group also confirmed the killing in another raid the following day of the group's previous spokesman Abu Hassan al-Muhajir.

The statement said the jihadist group's legislative and consultative body convened after the 48-year-old Iraqi-born jihadist chief's death.

"The Islamic State shura council convened immediately after confirming the martyrdom of Sheikh Abu Bakr al-Baghdadi, and the elders of the holy warriors agreed" on a replacement, said the seven-minute message.

The IS spokesman also issued a stark warning to the United States, whose President Donald Trump announced Baghdadi's death in a televised address from the White House.

"He died after running into a dead-end tunnel, whimpering and crying and screaming all the way," Trump said on Sunday, adding that Baghdad "died like a dog".

In the new audio message, the IS spokesman described Trump as "a crazy old man" and warned the US its supporters would avenge Baghdadi's death.

"Do not rejoice America," he warned, "the new chosen one will make you forget the horror you have beholden... and make the achievements of the Baghdadi days taste sweet".