A grenade has been thrown at police in the Kenyan city of Mombasa, killing one officer and wounding 16, officials say.
Muslim youths have been involved in running battles with the police since Monday after the murder of radical preacher Aboud Rogo Mohammed.
Mr Rogo, who the US accused of backing Islamist fighters in Somalia, was killed in a drive-by shooting.
Kenya's Prime Minister Raila Odinga has appealed for calm, saying the country should avoid an "inter-religious war".
"Let's act with restraint as law enforcement agencies get to the root of the matter," he said.
"We urge Muslims and Christians not to fight."
One person was killed and churches were attacked in clashes on Monday.
A senior police intelligence officer in Mombasa, Benedict Kigen, announced the grenade attack.
"They have attacked our officers... Two people are dead, one of them is an officer, the other is a civilian," Reuters news agency quoted him as saying.
Sixteen policemen were also wounded in the attack, according to the Red Cross.
Earlier, Ben Lawrence of Human Rights Watch told the BBC that he saw running battles between the police and protesters.
"I saw at the end of the street... billowing smoke and running battles between police and rioters. It came towards us, down the side street where I was located. People shut up their shops and ran in the opposite direction," he said.
"There's been shops set on fire, looting, police trying to control the situation with tear gas but so far apparently failing."
Hotel owners said the violence had badly affected Mombasa's tourism industry, the backbone of the city's economy, Reuters added.
"It's tricky to even take them [tourists] or pick them from the airport because the main highway from the airport is the epicentre of the chaos," said Mohammed Hersi, who runs the Whitesands Hotel.
Somalia's militant Islamist group al-Shabab condemned Mr Rogo's killing and said Muslims in Kenya should boycott next year's presidential election.
"Muslims must take the matter into their own hands, stand united against the Kuffar [non-Muslims] and take all necessary measures to protect their religion, their honour, their property and their lives from the enemies of Islam," it said in a statement.
However, police spokesman Charles Owino said al-Shabab killed the cleric in an attempt "to galvanise support among the youth", the AFP news agency reports.
"Rogo's murder was a well-planned attack by members of al-Shabab to gain sympathisers.... the al-Shabab have failed to get followers," he said.
Some of the rioters accused the authorities of being behind Mr Rogo's shooting, saying he had been the victim of a "targeted assassination".
Muslim leaders have denounced the violence, but many people are questioning how Mr Rogo could have been shot dead in broad daylight without anyone being arrested, says the BBC's Kevin Mwachiro in Mombasa.
Christians are also questioning why churches have been attacked, he adds.
Church leaders cancelled plans to hold a peaceful protest march on Tuesday for fear that it could trigger more violence, Reuters reports.
Mombasa, Kenya's second biggest city, has a majority Muslim population.
Kenya's Muslim Human Rights Forum said Mr Rogo was the second cleric on a "terrorism watch list" to be killed in Mombasa this year.
In April, preacher Samir Hashim Khan was abducted along with a blind colleague, Mohamed Bekhit Kassim, it said.
Mr Khan's mutilated body was later found in a national park near Mombasa, while Mr Kassim's whereabouts are still unknown, the rights group added.
Mr Rogo was on US and UN sanction lists for allegedly supporting al-Shabab, which is affiliated to al-Qaeda.
The UN Security Council imposed a travel ban and asset freeze on him in July, saying he had provided "financial, material, logistical or technical support to al-Shabab".
It accused him of being the "main ideological leader" of Kenya's al-Hijra group, also known as the Muslim Youth Centre, which is viewed as a close ally of al-Shabab.
He had "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 added.
In 2005, Mr Rogo was cleared on murder charges over the 2002 attack on a hotel where Israeli tourists were staying, which killed 12 people.