Indian Prime Minister Rajiv Gandhi, who is methodically addressing a succession of regional problems, appears close to a peaceful resolution of the long ethnic and religious conflict in the northeastern state of Assam.

Visiting Assam today, Gandhi said his government "very soon" would reach a negotiated settlement with Assamese dissidents who have demanded the deportation of immigrants from neighboring areas of India and Bangladesh. In New Delhi, Assamese dissident leaders said that they hoped for an early solution and that they had made progress in today's talks with government officials.

A peaceful settlement in Assam would help Gandhi -- who will be 41 this month -- maintain his broad popularity and confront criticism that he may be too inexperienced to tackle such massive problems.

The seven northeastern states -- which, unlike the recently reopened Punjab remain closed to most foreigners, including journalists -- are nearly surrounded by Bangladesh, Burma and China, and connect to the rest of India only by a narrow strip of territory. Assam provides 30 percent of India's domestic oil supply, hence New Delhi's special concern. The borders with Burma and Bangladesh are porous, and a small rebel insurgency operates in the state of Tripura.

"Peace in Assam would give emotional support to India and encourage all sides to pursue negotiation and compromise in other regional issues," said M.S. Krishna Rao, spokesman for the Home Ministry, which leads the government side in the Assam talks. "It would especially help the situation in the other northeast states, which face similar tensions because of the influx of immigrants," Rao said.

Rao declined to comment on specific details of the negotiations but said that newspaper accounts of the talks are "generally factual."

Such accounts have said the government may agree to a temporary disenfranchisement of immigrants who came to Assam after a certain year, perhaps 1967. In return, the Assamese are said to be willing to drop their demand for deportations, and both sides would agree to new elections in the state.

Gandhi's visit of several hours to Assam was the first by a prime minister since his mother, Indira Gandhi, toured the state amid civil violence in February 1983.

The 1983 upheaval, which killed at least 3,000 persons, was part of a continuing religious and cultural conflict between the mainly Hindu Assamese and the predominantly Moslem Bengali immigrants. The Assamese, many of whom live in tribes in the fertile Brahmaputra Valley, complain that the newcomers take up too much land and threaten Assamese culture.

Assamese students sparked a protest movement in 1979 that eventually forced the collapse of the state government. The 1983 violence followed a vow by native Assamese to stop state elections ordered by Indira Gandhi. At one point, Hindu tribesmen descended on villages of predominantly Moslem Bengalis and massacred about 800 to 1,000 of them with spears and hatchets.

In the 30 months since the election, the tension has remained high, with sporadic bombings and an assassination attempt against the state's chief minister, Hiteswar Saikia. The Assamese militants, organized into the All-Assam Students' Union and the People's War Council, have continued to call for the disenfranchisement and deportation of the immigrants.

But hopes for a solution have risen during the 10 months since Rajiv Gandhi took power after his mother's assassination. Indian and diplomatic observers give his decisiveness much of the credit for the recent progress. They cite the development as a parallel to his efforts to negotiate a solution for the Sikh-Hindu conflict in the northwestern state of Punjab.

"When Mrs. Gandhi was faced with a problem, she disliked making decisions. She would listen to her advisers and then take her own counsel, and one never knew when she might finally announce her decision," a western diplomat here said. "Rajiv hears his people and decides quickly -- often immediately in the Cabinet meeting," he said.

An account by Indian journalist M.J. Akbar that suggests that Indira Gandhi could have settled the Assam issue in 1980 on virtually the same terms now being discussed but that she hardened her offer at the last moment and scuttled the agreement.

"Mrs. Gandhi had mistaken the Assamese militants' desire to talk for weakness, and had convinced herself that she could outwit them by being tough over the table," Akbar wrote. In her talks with Assamese leaders "there was neither trust nor concession," he added.

Rajiv Gandhi, who five years ago gave up a career as an airline pilot to enter politics, has a relaxed and open political style that contrasts sharply with that of his mother.