COLOMBO, SRI LANKA, OCT. 12 -- Indian soldiers intent on capturing the last stronghold of Tamil rebels advanced on the northern city of Jaffna today against strong resistance, official sources reported.

Battles raged around the old Dutch fort in Jaffna and in the nearby villages of Chunnakam and Urumpirai, the Indian Embassy reported. Sources said commandos parachuted into the area northeast of Jaffna overnight.

J.N. Dixit, the Indian ambassador, said about 170 Tamil rebels had been killed since the push began Saturday. Sri Lankan military officials, speaking on condition of anonymity, put the rebel toll at 250.

Dixit said at least 14 Indian soldiers and paramilitary police had been slain. Five soldiers were missing, perhaps kidnaped by rebels, he said. About 2,000 Tamil guerrillas were believed to be defending Jaffna.

How many Indian troops were involved in the offensive could not be determined. It is their first since arriving to enforce a July 29 peace accord aimed at ending a four-year-old war with separatists among the Tamil minority that has taken more than 6,000 lives.

Between 12,000 and 15,000 Indian soldiers were sent to Sri Lanka. A Sri Lankan government official said about 1,000 elite Gurkha troops arrived today in Jaffna, a city of 150,000 people 186 miles north of Colombo, the capital.

Tamil rebel statements issued in Jaffna and in Madras, capital of Tamil Nadu state in southern India, accused the Indian peace-keepers of genocide against Tamils. The Liberation Tigers of Tamil Eelam, the largest rebel group, said more than 150 civilians had been killed. Indian officials denied the allegation.

Tamils came to Sri Lanka centuries ago across the strait that separates the island from the tip of India. They make up about 18 percent of its 16 million people. Most follow Hinduism, the predominant religion of India, and claim discrimination by Sri Lanka's Sinhalese majority, nearly all of whom are Buddhists.

India has nearly three times as many Tamils as the entire population of Sri Lanka and has tried for years to mediate a settlement of the ethnic conflict while allowing rebel groups to maintain exile headquarters on its territory.

Prime Minister Rajiv Gandhi got President Junius Jayewardene of Sri Lanka to accept the peace plan in July by guaranteeing that Indian troops would disarm the guerrillas.

Government estimates indicate nearly 13,000 Sinhalese have left their homes in the Tamil-dominated north and east since the latest violence began, fleeing to Colombo and Sinhalese-controlled areas in the south.

Dixit said most rebel bases in the north and east were surrounded. He predicted soldiers would need five or six days to subdue guerrillas in the Jaffna area and said about 300 had been taken into custody.

The offensive was launched late last week after India accused the Tigers of slaying more than 200 civilians, most of them Sinhalese. India was under increasing pressure to act because the Tamils were refusing to surrender weapons, as called for in the pact.

Indian military sources, speaking on condition of anonymity, confirmed the battles and said Jaffna town was surrounded by Indian troops on all sides.

N. Dinesh, the Tigers' political leader in Vavuniya district, said by telephone, "We are resisting the Indian invasion of Tamil Eelam. We will fight to the last man." Vavuniya is the first major town south of the Jaffna Peninsula.