Indian Prime Minister Morarji Desai resigned yesterday in the wake of mounting defections from his coalition government that left it with a parliamentary minority.

With Desai's resignation, the world's most populous democracy joins other South Asian nations facing mounting political instability on the eastern end of what U.S. national security adviser Zbigniew Brzezinski has called the "crescent of crisis."

Desai, 83, the fourth prime minister since India gained independence 32 year ago, said he would remain as head of a caretaker government until President Neelam Sanjiva Reddy names a new political leader to try to form a Cabinet.

During the past week, 13 of the government's 48 ministers resigned, taking with them almost 100 members of Parliament from the coalition of six widely disparate parties that joined to defeat Indira Gandhi's Congress Party 28 months ago and end her 19 months of authoritarian "emergency rule."

Defense Minister Jagjivan Ram, who was reported to have spent most of the weekend trying to persuade Desai to step down, emerged yesterday as the most likely candidate to form a new government. Ram, 71, is the undisputed leader of India's 100-million untouchable caste.

Desai's resignation came in the middle of the bloodiest year since India gained independence from Britain in 1947.

During the last six months, violence between Hindus and Moslems increased in at least a half-dozen scatered areas of the country, killing more than 150; inflation approached 28 percent for the year; labor strife mounted in key industries such as coal, steel, textiles, rails and power; and a federal police mutiny had to be put down by the Army with the loss of at least 25 lives.

The ascetic and deeply religious Desai reacted to these crises stoically, leading political observers in New Delhi to comment that his government was not doing little about the nation crumbling around it, but did not seem to care.

When asked at a press conference last month about "the crisis of confidence" in the government's ability to handle the nation's social and economic problems, Desai blamed the newspapers for fomenting the troubles.

Last week, with government defections mounting and its defeat apparently certain in a vote of no confidence scheduled for early this week, Desai told reporters, "These things keep going on all the time. I have faith that if something is going to happen, it will happen."

Yet the defections from his ruling Janata coalition continued. Just hours before Desai stepped down, Industries Minister George Fernandes a leader of the Socialist bloc in the Janata, resigned, along with two other ministers. Fernandes took 35 members of his party with him out of the coalition.

Fernandes said that Desai's resignation was the only way to save the disintegrating coalition, whose main glue had been its opposition to Gandhi. As her political strength appeared to wane in recent months, squabbles among competing ministers increased and Janata began to fall apart.

Defections from Gandhi's Congress (I) Party sparked the latest rift within the Janata coaltition as Indian politicians began talking of forging a new alliance of former Congress Party members and nonreligious elements within the government.

These secular parties criticized Desai for being unduly influenced by Hindu nationalist factions at the expense of minority groups.

Desai also was attacked for paying more attention to pet projects such as prohibition of alcoholic beverages and expanding the use of the Hindi language instead of trying to ease majority of India's 630 million people earn less than $150 a year.

President Reddy said he hopes to have a new government formed without dissolving Parliament and calling new elections.

Besides Ram, the other leading contender for prime minister is Charan Singh, the finance minister. He and Ram were Desai's rivals to form the government in 1977 when the Janata assumed control.

Desai, who dressed in simple, home-spun white cotton garb and took time out during a visit to Moscow last month to meditate and spin thread, was a disciple of Mahatma Gandhi's civil disobedience campaign to win independence from Britain. He was imprisoned three times in the 1930s - a badge of honor for an Indian politician of his generation.

During Indira Gandhi's emergency rule, he was imprisoned once again for being too vocal in his opposition to her authoritarian control.

Released in January 1977, he quickly sensed the opposition to her and worked to forge the Janata coalition that brought about her defeat on the issue of loss of liberty and forced sterilization.

Desai's resignation added to concern about the volatile region. Neighboring Pakistan, Afghanistan and Nepal are experiencing varying degrees of unrest. The shakiest nation is Afghanistan, where a pro-Soviet government is threatened by Moslem tribesmen.

In Pakistan, there was been simmering unrest since the execution of former prime minister Zulfiqar Ali Bhutto in April and elections are scheduled for November. Political turmoil in Nepal has forced the king to call a referendum for later in the year. CAPTION: Picture, MORARJI DESAI . . . blamed troubles on press