A member of the Soviet Politburo abruptly cut short his visit to the United States yesterday amid unconfirmed reports that Soviet leader Konstantin Chernenko had died.

Vladimir V. Shcherbitsky informed the State Department late yesterday afternoon that he and the other 29 members of a high-ranking Soviet delegation were ending their visit to the United States to return to Moscow as soon as possible.

Early this morning, Moscow Radio began broadcasting funeral dirges, which in the past has signaled a death in the leadership.

Shcherbitsky is one of 11 members of the ruling Politburo and his presence would be needed for a major vote or if a fellow member had died. Chernenko clearly has been ill for several months, but a number of other members of the ruling body also are in their seventies and eighties and in frail health.

If Chernenko is dead, he would be the third Soviet leader to have died within the past 28 months. Leonid Brezhnev's 18-year hold on Soviet power ended in November 1982. His successor, Yuri Andropov, ruled for only 15 months before he died in February last year to be succeeded by Chernenko.

Intense speculation on the subject of a new leader at the top of the Kremlin hierarchy has focused on whether power finally will pass from the old guard to a younger generation of Soviet leaders, represented by men such as Mikhail Gorbachev and Grigori Romanov.

Well-informed U.S. officials said the Shcherbitsky visit, which included talks with President Reagan during a six-day stay in Washington, had been going well and that there was no question of a dispute leading to the decision to cut short a visit to the West Coast by three days.

White House spokesman Robert Sims said Reagan was informed at 4 p.m. of the decision by the Soviet delegation to return home. Sims said the United States did not have an explanation for the decision and that there has been no official report from the Soviets to the U.S. Embassy in Moscow about Chernenko.

A spokesman for the U.S. mission to international organizations based in Geneva said that Vice President Bush, who is in the Swiss city to make a speech today, had received unconfirmed reports that the Soviet leader had died.

There also were reports in Washington that a member of the Soviet traveling party in San Francisco had said flatly that Chernenko had died, but U.S. officials familiar with the details of the visit refused any comment.

The State Department limited its public announcements to the sudden request of the Soviets to leave, and The Associated Press reported that one U.S. official, asked what the Soviets had said about their decision, responded: "They were asked, but told us nothing."

Washington Post correspondents Dusko Doder and Celestine Bohlen reported yesterday from Moscow that rumors about Chernenko's health had been rife in the Soviet capital throughout the weekend.

Soviet radio began to shift its programming to somber music about 4 a.m. today, and by 6 a.m. funeral dirges were being played.

But there were no announcements from the Kremlin.

Chernenko had missed a traditional meeting at the Bolshoi Theater marking International Women's Day Thursday night, but he had failed to make a number of anticipated appearances in recent months, leading Soviet officials finally to acknowledge that he was ill.

Doder and Bohlen reported that there was some unusually heavy weekend activity at the headquarters of the KGB, the Soviet secret police, but that otherwise it had the appearance of a normal Moscow weekend. There also was no unusual activity around key Moscow buildings early this morning.

Politburo member Vitali Vorotnikov, who has been on a visit to Yugoslavia, also interrupted his trip and departed for Moscow after an official dinner last night, Doder reported. Vorotnikov had been scheduled to return to Moscow today. The Yugoslav news agency Tanjug reported Vorotnikov's departure as a normally scheduled event, but diplomatic sources in the Soviet capital said he had cut short his visit.

Ever since Chernenko's health began to take a turn for the worse late last summer there have been a number of false reports that he had died. For months Soviet officials insisted that nothing was wrong or that he was not seriously ill, but when he failed to appear for an election speech for the parliament of the Russian Federation on Feb. 22, even the pretense that he was not seriously ill was dropped.

Chernenko, 72 when he took office, showed early signs of shortness of breath and other ailments, according to foreign visitors who met with him, and there were some reports that he was suffering from emphysema.

White House officials said a month ago that the U.S. intelligence community had come to the conclusion that the Soviet leader did have emphysema but that he was expected to live another six months.

The visiting Soviet delegation, the highest-ranking group of Soviet leaders to come to the United States since 1973, left Washington on Friday after a full round of talks with administration officials and members of Congress and contacts with the U.S. press.

After a weekend in Texas, they were scheduled to spend three days touring California before returning to Moscow on Wednesday. On arrival in San Francisco, however, the group went immediately to the Soviet Consulate and, according to U.S. officials, told the State Department they needed to leave immediately.

Shcherbitsky and his colleagues have been traveling on an official U.S. aircraft, however, and their own plane had flown to Havana after leaving the group in the United States, according to these officials.

The Soviet delegation now is scheduled to leave San Francisco at 5 a.m. today for a flight to New York and is to leave on the Soviet aircraft at 3 p.m. today.

The Soviets have stayed in the San Francisco consulate under tight security since their arrival, U.S. officials said, although there was some contact both with the State Department and with congressional liaison staff. Shcherbitsky and his group officially are here as a visiting parliamentary delegation, guests of the U.S. Congress.