Nathaniel Rosen, the American cellist who won a gold medal in the Soviet Union's Tchaikovsky competition, attended the University of Southern California school of the arts. His university was incorrectly listed in yesterday's edition.

Nathaniel Rosen, a 30-year-old cellist with the Pittsburgh Symphony, yesterday won Moscow's prestigious Tchaikovsky Competition gold medal, the first American instrumentalist to do so since Van Cliburn won for piano 20 years ago.

Rosen, a native of Los Angeles, achieved the victory after three rounds of competition against 57 other cellists from 20 countries, who performed a grueling series of auditions before concertgoers and international judges over the past three weeks. The third and final round of competition was over the weekend, but the results were not announced until yesterday.

However, when Rosen finished his final piece at the Tchaikovsky Conservatory in central Moscow, the audience of sophisticated listeners came to their feet with cries of "Bravo!" and waves of applause swept the hall, presaging his win.

Rosen has been principal cellist at the Pittsburgh, which is directed by Andre Previn, since last September. He had competed here once before, 12 years ago when he was 17, but without success. Last year he won the First International Cello Competition's Naumberg Prize in New York and felt himself ready to try again for the Tchaikovsky, perhaps the music worlds' most important prize.

Cliburn's victory here 20 years ago, to tumultuous public acclaim, was the start of one of contemporary America's most extraordinary and well-known careers on the concert stage.

Rosen, who studied for 10 years - from 1962 to 1972 - under the great cellist Grigory Piatigorsky, has been playing the instrument since the age of 6. ("it was a small model.") His father, David Rosen, a lawyer and "passionate amateur" violist, first introduced his son to the cello in hopes of forming three-quarters of a chamber quartet featuring the father, his two sons, and "one outsider who would be allowed to play." as Nathaniel Rosen recalled last night in an interview from his room at the Rossiya Hotel.

The introduction became a passion, the passion a career. He returned to Moscow, he said, to try again for the Tchaikovsky "because I could play on a much higher level than before." In 1966, he said, when he competed here. "I was learning a lot, participating fully in the events and examining the styles of the others. But this time, I was much more intense, concentrated."

The finalists' pieces were the difficult Tchaikovsky "Variations on a Rococo Theme" and Dvorak's cello concerto. Daniel Veis of Czechoslovakia and Mari Fugiwara of Japan were awarded second prize in the cello competition.

There are seven other Americans in the final rounds of other parts of the Tchaikovsky Competition: four in the violin segment, two in voice and one in piano. In 1974, American Eugene Fodor won a silver medal in violin together with two other violinists. No gold was awarded in violin that year.

Rosen and the other finalists will give a final performerance Friday night and then tour several Soviet cities, leaving here toward the end of July.

On Sunday, during the final cello round. Tass, the official Soviet news agency, declared "Rosen has been the greatest success among the American cellists. The music is characterized by broad musical thinking, technical perfection, wealth of colors." In another commentary, it said, he "displayed splendid techniques, a beautiful sound and confidently performed in all three stages of this difficulty contest, especially when he played Dvorak's concerto with orchestra."

Two Americans, Gary Hoffman of Bloomington, Ind., and Evelyn Elsing of Clarksville, Md., were awarded hoorary diplomas.

The cello is one of the most fascinating of orchestral instruments, capable in virtuoso hands of creating resonant melodic lines and rich full music of contrast against the louder and sharper instruments of the horns and strings. Such well-known virtuosos as the late Pablo Casals and such modern performers as Jacqueline Dupre have made the cello, despite the ungainly playing position it requires, into an instrument of some popularity in the United States.

Rosen said Monday night. "I like to think of myself as a descendant of a long line from the Davidoff school, the 19th-century fountainhead of the Russian cello style." He described this as a style that "stresses sound, variety of tone, color and expressiveness."

He studied cello at the University of California School of the Arts under Eleonora Schoenfeld and Lorenz Lessler, who was a Tchaikovsky laureate at the 1966 competition in which Rosen competed as a 17-year old.

His retinue here in Moscow has included his father, the attorney; his wife, jennifer, an accomplished cellist who performs professionally as Jennifer Langhan, and his 18th-century Montagnana cello, which he has had for the past five years.

Cliburn's success here was itself an event that helped create a mass audience for classical music in the United States, where a cultural explosion has occurred in the 20 years since that victory. Today, classical musicians enjoy wide recognition, their performances on records are heavily marketed by record companies, and their time sought after by the burgeoning number of professional orchestras.

Rosen has made two records and one has been released on the Desmar label, which he described as a small, "high-quality label" Monday night. It includes Chopin works for cello and piano, with Doris Stevenson, accompanist. It seems certain there will be other records in the future for Rosen.

But Monday night, he had no interest in talking about such things. "I'm just relaxing. I just feel fine. I hope to have many concerts in the future and as a musician be worthy of this great award."