* Riots sparked by disappearance of Islamist leader
* Shops looted and police use teargas, witnesses says
* Police say protesters hacked to death policeman (Adds more quotes, details)
STONE TOWN, Zanzibar, Oct 18 (Reuters) - Supporters of a separatist Islamist group in Zanzibar looted shops and fought with police on Thursday after their leader disappeared, witnesses said, the third outbreak of violence this year on the Indian Ocean archipelago.
Supporters of Sheikh Farid Hadi, a leader of the Islamic Uamsho (Awakening) movement who has not been seen since Tuesday, threw stones at police, blocked roads with cut-down trees and burned tyres in the island's main town.
"Police are everywhere and firing teargas. There is nobody around town and the shops are closed. It's a terrible situation," Said Salleh, 40, a businessman from Zanzibar, told Reuters by phone.
Witnesses said protesters looted shops and video footage showed a number of rioters holding machetes and hiding their faces with balaclavas.
Heavily armed police stepped up patrols late on Thursday and continued to engage in sporadic battles with rioters in Zanzibar's historic Stone Town.
"The streets are deserted ... Only heavily armed policemen are now patrolling the town. We are afraid to go out, we can still hear the sound of gunfire," Rukiya Khalifa, a resident of the historic Stone Town area, told Reuters.
The latest violence raised concerns of an escalation in religious tension in the predominantly Muslim island which is part of Tanzania but ruled by a semi-autonomous secular government.
Analysts said the Uamsho group has been gaining popularity following the disenchantment of supporters of Zanzibar's main opposition Civic United Front (CUF) party after its decision to form a government of national unity with the ruling Chama Cha Mapinduzi (CCM) party.
APPEAL FOR CALM
Fighting between police and Hadi's supporters, mostly youths, started on Wednesday, a day after the Uamsho leader disappeared.
"Our leader, Sheikh Farid, has been missing since Tuesday night and we don't know where he is as we speak," Uamsho secretary Abdallah Saidi told Reuters by telephone.
Earlier Saidi said he suspected that "perhaps" police may have been responsible, but as the violence continued into Thursday evening, police and Uamsho leaders held a joint news conference appealing for calm.
"It is very challenging for the police in trying to locate the whereabouts of the missing Uamsho leader, Farid, when we are forced to deploy a lot of our resources to tackle riots," Deputy Zanzibar Director of Criminal Investigations, Yusuf Ilembo, told reporters just outside Stone Town.
He said police were working with Uamsho leaders in the search for Hadi. Uamsho chairman Msellem Ali denied the group's supporters were involved in the violence.
Zanzibar police commissioner Mussa Ali Mussa earlier said Uamsho supporters had ambushed and hacked to death a policeman as he was walking home from guard duty on Wednesday evening. Saidi denied the group's involvement in the attack.
At least 10 suspects have been arrested in connection with the violence, police spokesman Mohamed Mhina said.
Witnesses said shops across the capital Stone Town remained closed for the second day in a row and residents stayed indoors, a scene reminiscent of 10 days of violent clashes between Uamsho supporters and police in May.
Back then riot police clashed with Uamsho supporters who had gathered at a mosque to pray for victims of a ferry disaster that killed 145 people.
In May Uamsho supporters set fire to two churches and clashed with police over the arrest of senior members of the movement. (Reporting by Fumbuka Ng'wanakilala in Dar es Salaam; Additional reporting and writing by Drazen Jorgic and Yara Bayoumy; Editing by Myra MacDonald)
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