In what amounts to a major artistic and diplomatic coup, the Kennedy Center and the Metropolitian Opera will jointly bring the Ballet Nacional de Cuba to this country for the first time next spring, with Alicia Alonso, the troupe's prima ballerina and founder-director, at its head.

The 85-member company will be seen in Washington first, arriving May 30 for a two-week engagement at the Kennedy Center after which it will perform at the Met starting June 13.

The state-supported Cuban company will thus become the first major artistic troupe from Cuba to appear in the United States since the two countries broke diplomatic relations in 1961. Kennedy Center's executive director Martin Feinstein said at a press conference yesterday that he sees the event as presaging a new era of cultural exchange with Cuba.

A State Department source said yesterday, however, that no great diplomatic significance should be attached to the Cuban ballet visit. Rather, he said, this was "part of the process of trying to improve relations with Cuba on a measured reciprocal basis.

"As a matter of general policy, we favor and encourage cultural, educational or scientific exchanges with Cuba. We welcome this development, and hope that some American artists or companies can soon be sent to Havana."

The initiatice for the visit came from Feinstein, acting on behalf of the Kennedy Center-Metropolitan Opera partnership announced last year. "This shows you what can happen when you pass an innocent remark to a lady, and what it can lead to," Feinstein remarked yesterday.

He was referring to a causual invitation he had extended to Alonso last year when she appeared in Washington in an American Ballet Theater gala program. Ten weeks ago, Feinstein said, a phone call from an intermediary indicated the company's readiness to perform here.

Feinstein spent a week in Havana last month observing the company in performace and choosing the repertoire for the visit. Officials of both the State Department - including Jospeh D. Duffey, then Assistant Secretary for Cultural Affairs and now chairman-designate of the National Endowment for the Humanities - and the Cuban Cultural Ministry gave their approval to the move.

In answer to a question, Feinstein said he thought the venture would not have been possible without the recent administration initiatives towards eased relations with Cuba. "Six months ago when I asked Alonso," he said, "there was no response."

Alonso, 56, regarded as one of the great classical ballerinas oif the century, stopped dancing in this country after the Cuban revolution, in order to help build the troupe she had founded in 1948 into a company of international stature.

Since then, the Ballet Nacional de Cuba has toured the Soviet Union, China, East Germany, Denmark, Canada and other nations, but has been seen here only on film. American dancers Cynthis Gregory and Ted Kivitt of The American Ballet Theater appeared with the Cuban Troupe in Havana in 1974, during the earliest stages of the "thaw." The following year, Alonso herself returned to the United States to dance with ABT after a 15-year absence.

For the company's Kennedy Center and Metropolitan Opera engagments next spring. Alonso will dance her most celebrated classic role, the title role in "Giselle."

She will also dance the title role in "Carmen," choreographed by Alberto Alonso to the Bizet music as arranged by Soviet composer Rodion Schedrin. In "oedipus Rex," which has choreography by Jorge Lefebre and a tape score by Leo Vanhurenbeck featuring Afro-Cuban music, she will appear as Jocasta.

"Oedipus Rex" is one of four U.S. premieres the company will offer. The others are: "Tarde en la Siesta" ("Late in the Afternoon"), a ballet about four sisters in colonial times in Cuba, choreographed by Alberto Mendez to a piano score by the late Cuban composer Ernesto Lecuona, whose own recording, made shortly before his death, will be used in the performance: "Canto Vital," with a score by Mahler and choreography by Azari Plisetski, brother of Soviet balerina Maya Plisetskaya and a former member of the Cuban troupe, and 'The House of Bernarda Alba," a setting of the Garcla Lorca tragedy choreographed by Ivan Tenorio to a score by Sergio Fernandez Barrose.

Feinstein will return to Havana to preview other classical and contemporary ballets which will be added to the programs, he said.

The Cuban government will pay the troupe's transportation costs to the United States, and the Kennedy Center and Metropolitan Opera will share the artists' fees and other production costs. Feinstein declined to give a projected budget total.

Feinstein also said both sides were aware that the visit may involve security problems, adding that "we are prepared to take the necessary provisions to guard against this."

No present plans exists for televising any of the Cuban performances, he said, but the matter would be given consideration. Even without TV, he indicated that prospects were good for a profitable engagement. He said other Cuban troupes also were being considered for possible future visits, but declined to discuss specifics.

Also present at the conference were Kennedy Center board chairman Roger L. Stevens; Anthony A. Bliss, executive director of the Metropolitan Opera Assn. and Jane Hermann, director of Special projects for the Met.