The 17-minute message follows rumours that Baghdadi was killed in a US air strike last week, Ansa reported.
"Make the volcanoes of jihad erupt everywhere," the message, released by al-Furqan media, a jihadi site, said.
"The crusaders' missiles will not stop our advance on Rome".
Several threats against Rome, the centre of the Catholic Church, have been made by the Islamic extremists.
In October, the group published a photo of its flag superimposed on the obelisk in St Peter’s square on the front cover of its propaganda magazine, ‘Dabiq’.
The magazine contained an article about the fight against "Rome" and "the Romans", terminology used to refer more widely to the West.
The magazine, which is published in several different European languages, is used by the organization to radicalize and recruit young people around the world, especially in the West.
Earlier this week, two people were detained after police found the Isis flag and a map of Rome in an apartment close to the capital.
Italy stepped up security in September following threats from the group, with Interior Minister Angelino Alfano saying that the threat posed by Isis is equal to that of terrorist organization al-Qaeda after the September 11th attacks against the US in 2001.