The impasse between the Kennedy Center and its orchestra erupted yesterday into a brief strike that paralyzed the center through midafternoon, threatened one performance of "West Side Story" and resulted in the 24-hour postponement of last night's scheduled opening of the India Festival of Music and Dance.

The strike began when talks between the center and orchestra broke off at about 4:30 a.m. yesterday after a marathon session with a federal mediator.

The job action continued for about 10 hours, with musicians picketing the center in midmorning. Several other unions, including stagehands and box office and Instant Charge workers, also walked out in support.

The most difficult issue concerned guaranteed employment for the musicians, and how any guarantees would apply to the 70 players. The musicians, represented by the American Federation of Musicians, maintained that in recent years, they have had significantly fewer work weeks and that their incomes have slipped accordingly.

The musicians had sought a 15-week guarantee for all 61 tenured musicians, beginning immediately.

Under the compromise, 10 work weeks will be guaranteed to 61 musicians in the first year, and 13 more weeks in the second, and final, year of the new contract. The agreement, which spokesman Frank Carnovale hailed as "achieving a new level of understanding with the center," does not affect the orchestra's separate contract with the Washington Opera. Allen G. Siegel, who bargained for the center, also praised the agreement.

This was the orchestra's first independent strike action, according to Richard Owens, the director of theater operations, who added that the musicians did go out once in the late 1970s "as part of an action at the same time the National Symphony was out."

Kennedy Center Chairman Roger L. Stevens said that during a meeting at noon yesterday to discuss the strike, "It became clear that, first, nobody wanted a strike, and, second, that a strike had become a reality.

"I didn't take part in the discussions until then," Stevens continued. "And it was becoming difficult." So much so, he said, that several leaders from other unions interceded with both sides in an effort to get talks under way again. Among them were Jack Ryan, head of the stagehands; George Koch, chairman of an interunion arts/culture committee; and Ron Richardson and Jake Boardman, of the hotel and restaurant employes Local 25.

Stevens said that he "sat down with a pencil and paper and came to the conclusion that it was much ado about nothing. We were having a very hard week and it was going to be very expensive. 'West Side Story' was doing very well, and we would have lost it for the rest of the run through Saturday . Last Monday was, in fact, the most profitable Monday we have ever had."

The center also faced the loss of the two-week appearance of the New York City Ballet, beginning Sept. 25. NYCB officials set a preliminary deadline of Thursday for solving the strike.

Siegel said that the wage package had essentially been settled earlier. "It amounts to 16 percent over two years . . ."

Laura Longley, spokeswoman for the Kennedy Center, said that ticket holders for last night's performance of "West Side Story," who were unable to attend because of uncertainty, could exchange their tickets for future performances. Ticket holders for last night's India Festival, which continues through Sunday, can exchange tickets or get refunds, Longley said.