An intense Indian diplomatic effort in recent days is reported to have breathed new life in the peace negotiations between the Sri Lankan government and minority Tamil rebels that broke down a week ago, seriously raising tensions in the Indian Ocean island nation.

Senior Indian government officials expressed optimism tonight that three days of talks between Indian Prime Minister Rajiv Gandhi and his foreign minister, Romesh Bhandari, with the chief Sri Lankan negotiator, Hector Jayewardene, may be on the verge of reversing the collapse of the peace talks that were being held in the neighboring Himalayan kingdom of Bhutan.

The peace talks, according to officials here, broke down Aug. 17 because of a fraying of the June 18 cease-fire that had been a condition for the Bhutan talks and, Indian officials said privately, the Sri Lankan government's refusal to make substantive proposals that would address the Hindu Tamil minority's complaints about domination by the island's Buddhist majority.

These sources said they were optimistic because Jayewardene, brother of the Sri Lankan President Junius R. Jayewardene, had delayed his departure from New Delhi repeatedly.

Originally he was going to stop in the Indian capital only to pay respects to Gandhi. That routine stop, however, turned into a new round of negotiations with the Indian government that included at least an hour of talks directly with Gandhi and more than 10 hours of talks with Foreign Minister Bhandari.

Gandhi not only has leaned heavily on the Sri Lankan government in recent days to come up with proposals that might defuse the crisis, but he also has sought to soften the most intransigent Tamil rebels now living in Madras, the capital of the southern Indian state of Tamil Nadu, by expelling three of the most militant opponents of the Bhutan talks.

Indian and Sri Lankan Tamil sources here said that the past days' talks had produced new Sri Lankan proposals on the sticky question of government decentralization, as well as vague promises that government troops would be restrained.

"There has been major progress," one senior Foreign Ministry official who is close to the talks said today. "There are now signs that the Sri Lanka government is prepared to make some real concessions that it had previously refused to advance at the talks in Bhutan."

The talks in Bhutan were brought about by Gandhi's personal mediation between the Sri Lankan president and representatives of the five Tamil guerrilla groups, most of them Marxist. The talks are regarded by western diplomats and Indian analysts as a last-ditch effort to avoid open civil war in Sri Lanka.

The violent confrontation between the nation's Sinhalese majority and Tamil minority is estimated to have cost several thousand lives in recent years.

Concerned by secessionist forces in his own vast and culturally diverse nation, especially in the volatile, Sikh-dominated Punjab, Gandhi has placed great importance on resolving the Tamil-Sinhalese conflict off India's southern coast, especially because of the Tamil population in five southern Indian states. They have identified with their fellow Tamils in the Sri Lankan conflict, and Tamil guerrillas are widely believed to train in and receive supplies from southern India.