* Officers say their methods are stamping out militancy
* Muslims who speak out against militants fear reprisals
* Police deny accusations of extrajudicial killings
* Rioters after Islamist death burned church
A Kenyan police crackdown on Islamists is fuelling Muslim resentment and moderate preachers say it undermines their efforts to counter recruiting by al Qaeda militants with links across the border in Somalia.
Smashing Islamist recruitment networks among its Muslim minority has become a priority for Kenya, however, as it tries to end attacks by Somali militants bent on punishing it for sending troops over the frontier to fight al Shabaab rebels.
The cost of failure was laid bare in September when al Shabaab gunmen, one of whom police say is a Kenyan from the port of Mombasa, raided the Westgate shopping mall in the Kenyan capital Nairobi. At least 67 people were killed.
Police say their tough approach, taken before Westgate but stepped up since, has limited the flow of would-be jihadists in and out of Somalia, citing a drop in the number of suspected militants they have tracked and arrested in the past year.
But Islamists, former militant sympathisers, independent security experts and diplomats, some of whom acknowledge short-term benefits from the police actions, say sweeping detentions and perceptions police are carrying out extra-judicial killings have fuelled Muslim resentment in the mostly Christian nation.
Police deny accusations of running anti-Muslim hit squads.
Moderate imams, particularly along the coast where most Kenyan Muslims live, have been attacked by Islamist radicals and some say they have been cowed into silence as a result.
Police tactics "are benefiting al Shabaab more than they are benefiting the government", said Akullah Khamis, a 33-year-old Muslim in Mombasa, Kenya's second city. He works with young people and non-governmental agencies and says he himself fended off a bid by al Shabaab to enlist his support three years ago.
Kenya's battle against militancy is seen as vital to the stability of east Africa's biggest economy, the gateway for regional trade and with a long coastline that has become a transit route for would-be jihadists trained in Somalia.
The United States, Britain and Israel, which fret about the reach of Africa's al Qaeda-aligned Islamists, have trained and equipped Kenya's anti-terror police and intelligence forces.
Mombasa county police commander Robert Kitur dismissed suggestions the force was being heavy handed or targeting the wider Muslim community: "We have never been brutal," he told Reuters. "People shouldn't generalise this is about Muslims."
"These are not Muslims, these are hooligans. We are going to deal with these people ruthlessly. We are just applying force when it is necessary."
However, one man accused by Western governments of aiding the militants believes widespread arrests, along with raids on mosques and the deaths of people during clashes with police, are helping al Shabaab recruiters.
"This being done to Muslims opens the eyes of the youth to al Shabaab being right," Abubakar Shariff, accused by the U.N. Security Council and the United States of raising funds and recruiting for al Shabaab, told Reuters at his Mombasa home.
Shariff, whose assets have been frozen by Western powers, denies the charges against him.
There is also new friction between majority Christians and Muslims, something that historically has been rare. Muslims, who make up about a tenth of Kenya's 40 million people, also complain of economic disadvantage in their coastal heartland compared to more prosperous central areas around the capital.
On Oct. 4, Muslim youths burned a Mombasa church after Islamist cleric Sheikh Ibrahim Omar died in a drive-by shooting - an attack some Muslims blamed on police. His mentor, Sheikh Aboud Rogo, was shot dead last year in similar circumstances.
Police deny wrongdoing and say they are investigating.
Two Christian pastors have been killed in recent weeks and one group of clergy has asked the government to issue rifles to protect their churches.
Joseph Sigei, police commander in the port of Lamu, near the Somali border, said the flow of suspected militants across the frontier has fallen sharply due to police tactics - only a quarter as many suspects had been detained trying to cross the frontier this year compared to last, he said.
Al Shabaab's losses in Somalia, where Kenyan and other African troops had driven them out of many cities and towns, had helped turn rebels into informants, Mombasa commander Kitur said, describing part of the police approach.
"(They) helped us with vital information about who, where and when radicalisation was happening," Kitur said.
But regional intelligence and diplomatic sources say recruitment and radicalisation of Muslims goes on, albeit more discreetly in the light of the police crackdown on Islamists.
One Western diplomat said a small group of "well-organised violent extremists" was able to drive their message home because of the weakness of mainstream Kenyan Muslim leadership.
"There is not a good counter-narrative coming from the moderates and moderate leaders," said the diplomat.
"BURN IN HELL"
For their part, moderate voices say their work has been undermined because the police make so many ordinary Muslims feel persecuted, fuelling suspicion of the authorities.
"Those of us who have stood up to speak against these things are viewed as traitors," said Hassan Suleiman Mohammed, an imam whom young Muslims threatened to kill as they fought police during riots on Mombasa's palm-lined avenues on Oct. 4.
Mohammed suspects that radicals who incited youths to roll over his car and jeer him in his mosque during Friday prayers also distributed a CD that named him and dozens of fellow imams "condemned to burn in hell" for opposing armed jihad.
Many Muslim leaders who support the government - if not police tactics - tread a fine line for fear of reprisals from al Shabaab and castigation by their communities, said Bryan Kahumbura, an analyst at the International Crisis Group.
"It is especially difficult to aggressively speak out against al-Shabaab down at the coast," he said of moderate Muslims. "So many people feel the government can't guarantee their own personal security and safety."