A grenade was thrown at a police truck in the Kenyan city of Mombasa Tuesday, in a second day of rioting over the killing of an extremist cleric linked to Al-Qaeda-allied militants, the Red Cross said.

Youths threw a grenade at a police truck on patrol in Mombasa, the organisation said, without giving details of any casualties.

Hundreds of angry youths threw stones, damaged cars and chanted slogans in support of slain preacher Aboud Rogo Mohammed, as police tried to contain them, an AFP reporter said.

The cleric, who was shot dead on Monday by "unknown people", according to the police, was on US and UN sanctions lists for allegedly supporting Somalia's Al-Qaeda-linked Shebab, including through recruitment and fundraising.

As the rioting stretched into a second day, the hardline Shebab fighters called on Kenyan Muslims to "take all necessary measures" to defend their religion.

"Muslims must take the matter into their own hands, stand united against the kuffar (unbelievers) and take all necessary measures to protect their religion, their honour, their property and their lives from the enemies of Islam," the Shebab said in a statement.

The cleric, popularly known as Rogo, was driving with his wife and children when gunmen opened fire on his vehicle, leaving it riddled with bullets. Images released by his supporters showed his bloody corpse slumped behind the wheel.

Shortly after his death furious protests erupted, with one person hacked to death, cars torched, businesses attacked and five churches looted or set on fire.