Alexei Kosygin, one of the Kremlin leaders who initiated East-West detente and served as Soviet premier for 16 years before resigning in October because of ill health, died early today at age 76, according to Soviet and diplomatic sources here.

The sources said Kosygin, known to have suffered from a heart ailment, died in the resuscitation ward of a Moscow hospital, presumably one serving Politburo members and other top Kremlin officials.

There was no official announcement of Kosygin's death here, but Moscow radio eliminated all jazz and light music from its program and broadcast classical music throughout the day.

The official silence on the passing of Kosygin, who became deputy premier 40 years ago and had remained ever since in the top echelon of the Communist Party and government, was ascribed by some observers to the fact that today was the 74th birthday of President Leonid Brezhnev and as such was not to be marred by bad news.

It is believed the death may be announced officially Saturday and that Kosygin's body will lie in state for two days, a customary honor for senior Soviet leaders, probably at the Central Army Club. His remains will be cremated, and he will be buried in the Kremlin wall alongside other highly honored Soviet leaders, these sources say.

There is some speculation that Kosygin's family may seek to have him burried instead in the Novodyeviche Cemetery, a few miles from the Kremlin, where Nikita Khrushchev and Anastas Mikoyan are interred.

Today's central press was filled with tributed to Brezhnev, who steadily forced Kosygin from sharing power after the two men engineered the ouster of Khrushchev in 1964. Kosygin, a man with a sad-eyed look, direct manner of speech, and considered to be among the most sophiscated of the Politburo, had served as premier from October 1964 to Oct. 23 of this year, when he asked to step down because of his deteriorating health.

He had been seen only twice in public during the last 12 months, the last time at the closing of the Moscow Olympic Games, and was said to be struggling unsuccessfully to overcome a serious heart attack in late 1979.

The Politburo more than a year ago had moved Nikolai Tikhonov into place as first deputy premier, and he was elevated to the premiership in October when Kosygin resigned.

As part of the continuing shakeup following Kosygin's resignation, the new agency Tass today announced the appointment of two new deputy premiers and the resignation of veteran Kosygin aide Vladimir Novikov, who has been deputy premier since 1965.

The new deputy premiers are Alexei Antonov, minister of the electrical equipment industry since 1965, and Ivan Bodyul, first secretary of the Communist Party in Moldavia since 961.

The death of Kosygin takes from the Soviet scene one of its most familiar faces. A native of Leningrad, Kosygin at age 15 volunteered for the Red Army, fought in the civil war, then attended a technical school. After working six years in Siberia, he returned to school to become a texile engineer.

When the massive industrialization efforts under Stalin began, Kosygin rose quickly, benefiting as well from Stalin's purges that decimated upper party echelons and offered Kosygin and others who could survive remarkable opportunities for advancement.

He served as mayor of Leningrad, then head of the national textile industry, and during World War II helped organize and direct the evacuation and supply of his home city during the 900-day siege by the Germans. He became a full member of the Politburo in 1948, suffered a brief setback a few years later when Stalin's final purge was beginning, but, like many other senior Kremlin aides, was spared disaster when Stalin died early in 1953.

Throughout the 1950s, Kosygin served as deputy premier, gaining wide knowledge of the country's economy, and sympathy for those who favored liberalizing its structure to allow for more factory incentive and flexibility. lWhen he moved to the pinnacle of power with Brezhnev as party secretary in 1964, Kosygin sought to implement some of these reforms.

But by the end of that decade, and in the aftermath of the invasion of Czechoslovakia, the conservatives headed by Brezhnev had thwarted most of Kosygin's intended reforms. At the same time, his role as an international statesman, in which he met with President Johnson at Glassboro, N.J., and played peacemaker at the Tashkent summit of 1965 between India and Pakistan, also went into eclipse.

In the early 1970s, Brezhnev became the world-traveling Soviet leader. The diminishing importance of Kosygin was underlined in 1977, when Brezhnev acquired the title of president as well as general party secretary, and in the years afterwards, seemed never tgo hesitate to blame Kosygin's planners and economists for many of the country's chronic shortages of food and other consumer goods.

Kosygin never made a point of defending himself or his vast and complex bureaucracy. Towad the end of the decade, he began have heart troubles, and once was reported to have nearly drowned after a heart seizure while swimming at his vacation dacha.

A widower rumored to have remarried some years ago, Kosygin is survived by daughter Ludmilla, who is married to Dzherman Gvishiani, deputy chairman of the State Committee on Science and Technology.