A radical Kenyan Muslim cleric, blacklisted by the US and the UN for allegedly supporting Somalia's al-Qaeda-linked al-Shabab, has been shot dead, his wife said.

Aboud Rogo Mohammed was killed on Monday in the Kenyan coastal city of Mombasa.

Following the killing, protests have erupted in Mombasa in which one person has been killed.

"A car behind us aimed at my husband, they shot him on the right side," Haniya Said, the widow, said screaming in grief.

Witnesses said the car was riddled with bullets.

A photograph released by his supporters showed Mohammed's bloody corpse slumped behind the wheel of a car.

"He died as we rushed him to hospital. Why have they killed my dear husband?" Said said, before she and her children were taken to the hospital.

The cleric was travelling in a car with his wife and child when gunmen attacked his car, Al Jazeera's Peter Greste reported from the Kenyan capital Nairobi.

"As a result of this, the cleric's supporters have been rioting in the streets," he said. "We understand that they've attacked a number of government vehicles, they've burned some other vehicles, and the situation is still fairly out of control right now."

Riots erupt

Thousands of protesters gathered in Mombasa following Mohammed's killing, blocking off streets around the mosque where he had often preached.

Kenyan police fired teargas to disperse people protesting, according to Reuters news agency.

They set fire to vehicles and chanted slogans in his support, while others reported running battles with the police.

Several protesters were injured, and the Mombasa to Malindi highway has been closed by demonstrators.

A police source confirmed Mohammed had been killed.

"He has been shot dead, he was in a vehicle with his family including wife and children when they were attacked," the source told AFP news agency.

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Joseph Kitu, the regional deputy police chief, confirmed a shooting incident, but gave no further details.

Mohammed was placed on a US sanctions list in July for "engaging in acts that directly or indirectly threaten the peace, security or stability of Somalia", specifically for recruiting and fundraising for al-Shabab.

The United Nations Security Council placed a travel ban and asset freeze on the cleric in July, saying he had provided "financial, material, logistical or technical support to al-Shabab".

He was the "main ideological leader" of Kenya's Al Hijra group, also known as the Muslim Youth Centre (MYC), the UN said in July.

The group is viewed as a close ally of the al-Shabab in Kenya.

Mohammed "used the extremist group as a pathway for radicalisation and recruitment of principally Swahili-speaking Africans for carrying out violent militant activity in Somalia," the UN said.

MYC leader Sheikh Ahmad Iman Ali, in a message posted on Twitter, said: "We are on the right track when our leaders get shahadah [martyrdom]."

"He will remain in our hearts forever," the MYC added.

Another message offered the grim warning that the "kuffar [unbelievers] will pay" for his death.