The National Symphony Orchestra will spend a week in June at the Casals Festival in Puerto Rico and will tour southern Europe later in the summer, it was announced at a press conference yesterday.

No precise dates were given for the European tour, for which details are still being negotiated, but it is expected to begin in the first week of August.

And music director Mstislav Rostropovich, who on earlier occasions has talked about his desire to take the NSO to play in the Soviet Union, was also asked yesterday whether he expects to see this happen in the current atmosphere of glasnost.

Rostropovich answered cautiously but did not exclude the possibility. "First must be coming invitation," he said. "After that, I talk. But not yet."

The Puerto Rican tour will include concerts conducted by Rostropovich on June 14 and 19, concerts conducted by James Conlon on June 15 and 16 and a free chamber music program given by members of the orchestra on June 17.

The free concert will include a new work, commissioned by the cello section of the NSO, by David Ott, whose Concerto for Two Cellos and Orchestra, given its world premiere by the NSO earlier this month, was one of this season's highlights.

A second Ott work, written for 12 cellos, will have its first performance at the First International Cello Congress here in early June. Rostropovich said the NSO cello section "is, in my opinion, the best in the world. But I do not want to insult other orchestras; let's say it's one of the best in the world."

Rostropovich mentioned a number of new works commissioned by the orchestra. But except for the still untitled Ott composition, no performance dates were announced because the works are still in progress.

One work is by George Crumb, one of the most respected living American composers, who has asked for more time to complete it. "When he finishes it," Rostropovich said, "we will play it." Other works include a Concerto for Double Bass and Orchestra by the witty, technically brilliant double bass virtuoso Jon Deke, a violin concerto for NSO concertmaster William Steck by Leonard Rosenman, and a piano concerto for the orchestra's keyboard player Lambert Orkis by Richard Wernick.

A work not commissioned by the orchestra but given to it in a surprise gesture is the "Stykhira" (Liturgical Hymn) of Rodion Shchedrin, which will have its world premiere here March 3. Rostropovich said Shchedrin is not expected to be here for the premiere but will try to be present at a repeat performance March 8.

A number of familiar Rostropovich specialties have been scheduled for the subscription season next year, including Aulis Sallinen's Symphony No. 5, "Washington Mosaics"; Tchaikovsky's Fifth Symphony, Serenade for Strings and "1812" Overture; Shostakovich's Seventh Symphony ("Leningrad") and the suite from his opera "Lady Macbeth of Mtsensk."

No announcement was made as to whether these works would be recorded under the orchestra's new contract with Erato Records, but it seems likely that at least some of them will be.

Other prime candidates for recording in next season's scheduling may be Prokofiev's "American Overture" and sound-track music for "Ivan the Terrible," both of which the orchestra will be performing for the first time. For the "Ivan the Terrible" music, the orchestra will be joined by the Choral Arts Society, mezzo soprano Cleopatra Ciurca and bass Paul Plishka.

Rostropovich will open the season in mid-September with a 70th birthday tribute to Leonard Bernstein, and will have Frederica von Stade as his guest artist for the first week of October in Ravel's "Sheherazade." Another notable vocal soloist will be baritone Hakan Hagegard, with Rostropovich conducting Mahler's "Songs of a Wayfarer" and four "Ru ckert" lieder.

Guests next season will also include cellist Janos Starker, violinists Viktoria Mullova, Elmar Oliveira, Joseph Swensen and Pinchas Zukerman (who will also conduct) as well as NSO concertmaster Steck. Guest pianists will include Vladimir Ashkenazy, Emanuel Ax, Cristina Ortiz, Maria-Joao Pires and Andre' Watts. French horn virtuoso Barry Tuckwell will be a guest artist, along with tenor John Aler, when James Conlon conducts Britten's Serenade for Tenor, Horn and Strings.

Also scheduled as guest conductors are Rafael Fru hbeck de Burgos, Gunther Herbig, Sir Neville Marriner, Kazuyoshi Akiyama, Gerd Albrecht, Paavo Berglund, Zdenek Macal, Georges Pre~tre, Alessandro Siciliani, Tama's Va'sa'ry and Hugh Wolff.