NAIROBI (Reuters) - Two policemen were shot dead on Friday at a market in the eastern Kenyan town of Garissa, a base for security forces fighting insurgents in neighboring Somalia.

The policemen, among a group of five officers, were on a routine inspection at the town's main market when they were attacked, said Garissa police chief George Losku.

"The attackers shot dead two of the officers while the other three engaged the attackers in a gunfight," he said.

It was not immediately clear if the attackers were connected to Somali Islamist militants and their sympathizers, blamed by the government in Nairobi for a surge in grenade and gun attacks in the past year following Kenya's deployment of troops into Somalia to battle al Qaeda-linked al Shabaab rebels.

Garissa, a market centre for trade in camels, donkeys, goats and cattle located 200 km (120 miles) from the Somali border, is an operating centre for the military mission and a target for the insurgency - one of the Kenyan government's major headaches ahead of a March election.

Kenyan soldiers and Somali forces seized Kismayu, al Shabaab's last major urban stronghold in southern Somalia, six weeks ago, driving the militants out.

In July, attacks on two churches in Garissa killed 17. Since then there have been sporadic grenade attacks.

Separately, in the southern coastal city of Mombasa, a man threw a grenade at a local administrator's office, wounding three people, including the official, police said.

"These are al Shabaab operatives who ran away from Somalia after the invasion of our forces, especially in Kismayu," Robert Kitur, Coast region deputy police chief, said.

The attack took place in Kwale, 20 km (12 miles) south of Mombasa, an area known as a stronghold for the separatist Mombasa Republican Council (MRC), which is campaigning for the secession of Kenya's Indian Ocean coastal strip, a tourist and trade hub.

The government has intensified a crackdown on MRC members and supporters in recent months, though some senior members have recently been released on bail.

(Reporting by Abdisalan Ahmed in Garissa and Joseph Akwiri in Lamu; Writing by Yara Bayoumy; Editing by Louise Ireland)