NAIROBI (Reuters) - A nine-year-old boy was killed and three other children wounded when a hand grenade was thrown into a Sunday school session in a church in the Kenyan capital Nairobi, police and medical staff said.

Kenya has suffered a series of grenade attacks since it sent troops across the border into Somalia last October in pursuit of Islamist al Shabaab militants who it blamed for kidnapping its security personnel and Western tourists.

The attack on the church came days after Kenyan troops launched a surprise offensive on the southern Somali port of Kismayu, the last stronghold of the al Shabaab, forcing the rebels to flee.

Police said attackers threw the grenade into the Sunday school service in St. Polycarp's church on Nairobi's Juja Road.

The grenade exploded, spraying the children with shrapnel and fatally injuring the boy.

"We suspect this blast might have been carried out by sympathizers of al Shabaab," said deputy police spokesman Charles Owino.

"These are the kicks of a dying horse since, of late, Kenyan police have arrested several suspects in connection with grenades," he added.

Masked assailants launched simultaneous gun and grenade raids on two churches in the northern town of Garissa in July, killing at least 17 people.

(Reporting by Duncan Miriri and Humphrey Malalo, editing by Andrew Heavens)