BALTIMORE (AP) _ Three musical groups from the Peabody Conservatory, the nation's oldest school of music, have been invited to tour the Soviet Union next fall, school officials say.

The invitations come on the heels of an announcement that the Baltimore Symphony Orchestra will visit Moscow and Leningrad next month.

The conservatory groups will perform in Moscow and Leningrad for 10 days, beginning Nov. 26, in tours that mark the first time in more than 20 years that an American music school has sent performers to the Soviet Union.

The invitations to the Peabody Symphony Orchestra, Peabody Honors Quintet and the Peabody Ragtime Ensemble, a group of Peabody graduates, were planned for performances in conjunction with a Smithsonian Institution exhibit, ''New Horizons: American Painting 1840-1910.''

While the Baltimore Symphony Orchestra will perform only two American pieces for Soviet listeners, the Peabody groups will play only American music from the period coinciding with the exhibition works.

The programs include works by Charles Ives, Aaron Copland, Charles Martin Loeffler, Edward MacDowell and Virgil Thomson. Much of the music hasn't been performed in the Soviet Union previously.

Robert Pierce, director of the school founded in 1856, expressed confidence that Peabody could raise the $200,000 needed for the trip. ''This is a real coup for the city of Baltimore and the state of Maryland. I'm sure that we will attract donors.''

Johns Hopkins University also will organize a symposium at Moscow's State Tretyakov Gallery to coincide with the exhibition opening Nov. 16, Pierce said.

The musical invitation derived from a 1983 invitation to the Smithsonian to exhibit in the USSR. Cooled relations between the superpowers delayed the show until the Geneva summit led to the resumption of cultural exchanges.