Konstantin U. Chernenko, who ruled the Soviet Union for 390 days, was buried with military honors in Red Square today in a traditional Russian ceremony attended by scores of world leaders.

It was the third funeral of a Soviet leader in less than 2 1/2 years. Once again the entire country came to a five-minute standstill as Chernenko's body was lowered into a grave behind the Lenin Mausoleum, at some distance from the sites where his predecessors, Leonid Brezhnev and Yuri Andropov, were buried.

Immediately after the funeral, Mikhail Gorbachev, the new Soviet leader, plunged into a series of meetings with foreign leaders, including a 90-minute session with Vice President Bush and Secretary of State George P. Shultz.

After their talk, Bush said President Reagan will meet with the new Soviet leader whenever the Kremlin is ready.

"If there ever was a time when we could move forward with progress in the last few years, I'd say that this is a good time for that," the vice president said. Details on Page A27.

Before the private meetings with foreign leaders, Gorbachev hosted a reception in St. George's Hall in the Kremlin for all foreign delegations that attended the funeral.

In his subsequent meetings, Gorbachev touched upon many of the major areas of interest to Moscow. In addition to his lengthy talk with Bush and Shultz, he met with British Prime Minister Margaret Thatcher, French President Francois Mitterrand, Indian Prime Minister Rajiv Gandhi, who is also head of the Nonaligned Movement, Nicaraguan President Daniel Ortega and all the leaders of the Warsaw Pact.

Gorbachev, who succeeded Chernenko as general secretary of the Soviet Communist Party, the country's most powerful political post, led other Kremlin leaders to the graveside to throw handfuls of earth into the grave.

Gorbachev, delivering a funeral oration from atop the Lenin Mausoleum, hailed Chernenko as a "true son of our party and people, a steadfast fighter for noble communist ideals, and a prominent party and state figure." He singled out Chernenko's "major peaceful initiatives aimed at terminating the arms race" and pledged to "continue stepping up efforts in this direction." Gorbachev's speech was moderate in tone and included no denunciations of the United States.

On domestic policies, Gorbachev signaled that he intends to push for Andropov's reformist program, specifying that the strategic course of the party had been set at the 26th party congress and at the Central Committee plenum in November of 1982. It was that plenum that brought Andropov to power.

"Satisfying the growing requirements of Soviet people, improving the conditions of their work and life, have always been and remain the major concern of the party and the state," he said.

During the reception at St. George's Hall, Gorbachev was accompanied by Prime Minister Nikolai Tikhonov, Foreign Minister Andrei Gromyko, and First Vice President Vasily Kuznetsov. Gorbachev seemed to be at ease and chatted with several prominent foreign visitors, spending the most time with Japanese Prime Minister Yasuhiro Nakasone

Tikhonov held a series of private half-hour sessions with foreign dignitaries.

In his funeral oration, Gorbachev reaffirmed Moscow's commitment to a policy of peaceful coexistence. He asserted that socialism will eventually prove its advantages as a social system.

"But," he said, "it will prove them not by the force of arms but by force of example in all fields of society's life -- economic, political and moral."

The funeral itself was a spectacle that has become familiar in Red Square. Shortly after 12:30 p.m., Chernenko's body was carried out of the Hall of Columns, where it had been lying since Monday, and was placed on a gun carriage for the short trip to Red Square.

With sounds of Chopin's "Funeral March" echoing throughout central Moscow, an olive-green military scout vehicle towed the carriage with the closed coffin, draped in red and black, in a resplendent procession.

The cortege was preceded by a procession of high-ranking officers carrying huge wreaths and bearing Chernenko's medals and awards. Relatives and close friends followed, then members of the Politburo and other senior officials.

Portraits of Chernenko trimmed in red and black bobbed above the crowd in Red Square as the procession with its column of mourners, marching soldiers and a military band filed past.

The procession halted before the red-marble Lenin Mausoleum, where the coffin was opened and placed on a bier facing the mausoleum. After the speeches, the open coffin was carried to the grave. The country's leaders walked behind the coffin, which was carried by armed officers.

Following the ancient tradition of the Russian Orthodox religion, Chernenko's wife, Ana Dmitrievna, kissed the dead leader's forehead before the coffin was closed.

With the sounds of Kremlin bells, factory and ship sirens and artillery salutes ringing from the Pacific to the Baltic Sea, Chernenko's body was lowered into the ground.

The 10 surviving members of the Politburo stood at attention, their arms raised in salute, as the coffin was lowered.

As the Soviet national anthem was played, the flag atop a Kremlin building was raised from half to full staff.

Gorbachev and other members of the leadership returned to the mausoleum for the traditional military parade.

Today's lineup atop the mausoleum provided no clues as to relative strength of various personalities in the new leadership. Politburo member Viktor Grishin, 70, who also delivered a funeral oration, was placed to the right of Gorbachev, 54, indicating that he may become, at least for the time being, the party's second secretary in charge of ideology.

Judging by his public actions and pronouncements so far, the new Soviet leader appeared to be moving quickly to assert his preeminence in the leadership. Diplomatic observers here said they were impressed by his self-confident and smooth performance.