Music Director Mstislav Rostropovich yesterday announced most of the details of the National Symphony Orchestra's next season -- including a proposed three-week tour of major European capitals.

"A European tour has been contemplated for some time. It is consistent with the report of the task force on the NSO. It is estimated that it will cost around a half million," the orchestra's president, Leonard Silverstein, explained yesterday, adding that the board's vote to undertake it was unanimous. "We are working to arrange the financing without harming our ongoing financial planning here at home," he said.

Next season's plans for Washington include 10 weeks under Rostropovich, with Principal Guest Conductor Rafael Fruhbeck de Burgos taking six weeks. Leonard Bernstein, who is conducting the orchestra next week, will be back for two weeks, as will Exxon/Arts Endowment Conductor Hugh Wolff.

The season will open under Rostropovich on Sept. 15 with the world premiere of a new overture by Sir William Walton, who will celebrate his 80th birthday on March 29, 1982. Rostropovich, also will conduct a three-week Tchaikovsky festival including a complete performance of the opera, "Iolante," starring Galine Vishnevskaya and Nicolai Gedda.Rostropovich will close the season with the first performance of a major work for chorus and orchestra commissioned by the orchestra from Pulitzer Prize winner Jacob Druckman.

The season's pianists include Cecile Licad, recent winner of the Leventritt Award; Jorge Bolet; Vladimir Ashkenazi; Andre Watts, and Nicole Henriot. Violinists will be Yehudi Menuhin, Uto Ughi, Anne-Sophie Mutter, Miran Kojian, and three to be announced for performances of a Szymanowski concerto, the Brahms Double Concerto, and work still undecided.