The National Symphony Orchestra will go to Mexico this spring and to Japan and South Korea next year, music director Mstislav Rostropovich announced yesterday. He also outlined details of the symphony's first two recordings under his baton.

The Mexican tour, from May 10 to 17, is under the auspices of the Serventino Festival at Guanajuato and replaces the trip that was canceled last fall because of the musicians' strike.

The symphony will go to Japan under the auspices of the Osaka Festival in 1980 from April 4 to 24. They will play 12 concerts in Japan in Tokyo, Nagoya and Osaka and two in the new concert hall in Seoul, Korea.

"We now need to show our art in other halls and other countries," said Rostropovich.

Rostropovich said the symphony's first two recordings under his baton will be issued late in March or early April. They are the Tchaikovsky Violin Concerto with Isaac Stern and the Schumann and Chopin F Minor Concertos with Martha Argerich, both on Deutsche Grammophon. "I have heard both of them," he said, "and they are of very high quality."

Rostropovich also announced that guest conductors for the coming season will include Leonard Bernstein, with the title of Distinguished Visiting Conductor, for four weeks: Antal Dorati, returning in his final season as principal guest conductor, for five weeks; Rafael Fruhbeck de Burgos, two weeks; Kiril Kondrashin, two weeks; and Erich Leinsdorf, Robert Shaw and Christian Bades, one week each.

Rostropovich said Badea, who has been with the NSO for two seasons as assistant conductor, will leave that position next year. "His career is coming very fast, he has many requests to conduct. The National Symphony cannot apply brakes to any career," he said. "In his place, we will hold auditions in July among top young conductors and would like to have not one but three, for three months each, and give them real chances to appear with orchestra."

Soloists in the coming season will include pianists Alicia de Larrocha, Martha Argerich, Eugene Istomin, Radu Lupu, Horacio Gutierrez, James Tocco, Ilse von Alpenheim and Bruno Leonardo Gelber, Rostropovich said.

Violinists will include Sophie Mutter, whom Rostropovich called "perhaps the greatest miracle since Menuhin. She is 14, 15. I heard her at a concert for Karajan's 70th birthday and I just not believe. When I say she must play with National Symphony, she say, 'Please speak to my parents.'"

Other violinists will include Elmar Oliveira, the first American violinist ever to win a gold medal in the Tchaikovsky Competition in Moscow, and Itzhak Perlman. Trumpeter Maurice Andre, oboist Sara Watkins, English hornist Thomas Stacy, and cellists Luis Claret and John Martin also will be soloists.

Major works which were not heard during the present season because of the strike will be played next year. These will include the Mahler Seventh Symphony and Strauss's "Don Quixote," for which Rostropovich said they received numerous phone requests.