Sri Lankan President Junius R. Jayewardene today promised amnesty to Tamil separatists fighting a fullscale insurrection in the Northern and Eastern provinces of his country if they will lay down their arms.

"I will provide them amnesty" if they stop fighting, Jayewardene said as he left here after three days of talks with Indian Prime Minister Rajiv Gandhi seeking ways to end the bloodbath that has raged in neighboring Sri Lanka for more than two years.

The talks here yesterday and today took place against a backdrop of intensified violence in Sri Lanka that left at least 80 persons dead in raids by Tamil militants, who form a minority on the island nation off the southeastern tip of India, and by members of the Sinhalese majority.

United News of India reported from the Sri Lankan capital, Colombo, today that eight armed men killed 17 Tamil passengers pulled off a bus near Trincomalee in Sri Lanka's Eastern Province. The raid reportedly was in reprisal for Tamil attacks Friday and Saturday in which two Sinhalese villages were burned.

While no specifics were given on how to end the bloodshed in Sri Lanka, a joint statement indicated a new feeling of urgency on the part of both governments to end the violence and achieve a political solution. It called for "immediate steps" to end the fighting and move toward a political settlement "acceptable" to Tamils and Sinhalese.

Jayewardene later said India could "very much" help to solve the problem.

"To the extent that our good offices can be used, they are available," Indian Foreign Secretary Romesh Bhandari said.

Both Sri Lanka and India termed the talks "positive" and "useful," and a high-ranking Indian official said they were more constructive than a meeting 11 months ago between the leaders of the two countries.

Since that meeting, however, Indira Gandhi was assassinated, and India now faces an intensifying separatist problem of its own from Sikh fundamentalists in the Punjab.

In his talks with Rajiv Gandhi, Indira Gandhi's son, Jayewardene was reported to have emphasized that India and Sri Lanka should cooperate in their own national interests to fight terrorism. He has accused India in the past of helping Tamil terrorists by giving them sanctuary and allowing them to run training camps in India.

The violence in Sri Lanka is a political problem here because of the close links between the Tamils in Sri Lanka and fellow Tamils who live across the narrow Palk Strait in the Indian state of Tamil Nadu. Moreover, a religious connection links Indian and Sri Lankan Tamils, who are Hindus; the Sinhalese are Buddhists.

Jayewardene was reported to have asked Gandhi to end any sanctuary that India was providing Tamil insurgents.