Aboud Rogo Mohammed, who the United States accused of advocating the radicalisation and recruitment of non-Somali Africans by the al Shabaab militant group, was shot dead on Monday and buried shortly afterwards.

Rogo was facing charges of planning acts of terror and importing illegal weapons.

"He was driving in a personal car with other four other occupants. Unknown gunmen attacked his vehicle ... sprayed it with bullets and killed him on the spot," Robert Kitur, deputy police chief for the region said.

"They must have been targeting him, and must have been trailing him for a while."

Kenyan police fired rubber bullets in the air and teargas to disperse protesters in Mombasa, Kenya's main port city and a popular tourist destination. The city has a high population of Muslims.

Hundreds of protesters stoned cars along the main highway linking Mombasa to Mali, another tourist town, and burnt tyres to prevent cars from using the road.

They smashed their windscreens and headlamps, chanting slogans in Arabic before they were dispersed with teargas.

Others vandalised at least four churches on the outskirts of the city, breaking chairs and turning an altar upside down.

Shops in Mombasa were shuttered as armed police patrolled streets usually full of shoppers and foreign tourists as many people barricaded themselves indoors.

The protesters blamed police for the killing of Rogo.

"These are police who have killed our innocent Sheikh. They have shot him dead. They imposed on him terrorism charges, arrested and charged him, now they fear the court will release him, and have decided to end his life," Suleiman Athman, a Muslim youth taking part in the demonstration, said.

"It's an attack on Muslims, and we will not take it lightly."