* Makaburi openly supported Somali militants al Shabaab
* Drive-by shooting condemned by Muslim groups
* Armed police step up patrols in port city of Mombasa
By Joseph Akwiri
MOMBASA, Kenya, April 2 (Reuters) - Two prominent Kenyan Muslim rights groups threatened on Wednesday to stage street protests in the port city of Mombasa unless the government met a Saturday deadline to say who had killed a prominent Islamist.
The ultimatum was issued a day after the drive-by shooting of Abubakar Shariff, also known as Makaburi, who the United States and U.N. Security Council accuse of supporting the Somali militant group al Shabaab.
Mombasa-based Muslims for Human Rights (Muhuri) and Haki Africa have in the past both accused Kenya's Anti-Terror Police Unit (ATPU) of carrying out extra-judicial killings of well-known Muslims, a charge the police have always strongly denied.
Makaburi had told journalists he expected to be assassinated by the police. Makaburi's close ally and friend, preacher Aboud Rogo, was killed in a drive-by shooting in 2012.
"Whichever way we look at it, the government is culpable for either killing Makaburi or for failing to prevent his killing," said Hussein Khalid, director of Haki Africa, a rights group.
Interior Minister Ole Lenku denied government involvement in Makaburi's death and said an investigation had been launched.
"We are certain those criminals will be brought to book and dealt according to law," Lenku said.
Mombasa was calm but tense on Wednesday. Many businesses shut in the city's flashpoint area of Majengo. Trucks full of armed police patrolled palm-lined streets and surrounding areas.
When Rogo was shot dead in 2012, the killing caused several days of riots. The same happened when Rogo's protege was killed in almost identical circumstances in October 2013.
Muslim youths also clashed with police for three days in February after a man was killed during a police raid on a mosque used by firebrand preachers in the Majengo area.
Khalid, flanked by Muhuri members, said the government had three days to "unravel the mystery" of Makaburi's death.
"Failure to (do so means) we shall go to the streets in protest as allowed under our constitution," he added.
The east African country, the region's largest economy, is still reeling from an al Shabaab attack on a shopping mall in Nairobi in September in which at least 67 people were killed.
Security sources say Makaburi had become a leading member of al-Hijra, a Kenyan affiliate of Somalia's al Shabaab.
Muslims accuse Kenya of using heavy-handed tactics to try to dismantle Islamist networks, stirring anger in the Muslim population along the coast who say they are being harassed.
"These kind of killings are not helping. They are only fanning hatred and resistance. Government should find ways of stopping the reckless killings," said Sheikh Mohammad Dor, chair of the Council of Imams and Preachers of Kenya.
(Additional reporting by Humphrey Malalo in Nairobi; Writing by Drazen Jorgic, Editing by Edmund Blair and Angus MacSwan)