A two-and-a-half-hour negotiating session in the offices of the Federal Mediation Service yesterday failed to budge either side in the four-day-old strike by musicians of the National Symphony Orchestra.

When the meeting ended exactly where it had begun, according to both players and management, federal mediator Harold Mills set the next meeting for Wednesday, Oct. 4.

In the meantime, the symphony management has not yet canceled the six concerts scheduled in Mexico next week. A spokesman for management said yesterday, "Our deadline is not until Thursday evening. Anything could happen."

After the session with the mediator, which was the first meeting held since the strike began at midnight last Saturday, William Foster, chairman of the players' negotiating committee, said, "The union was told by the chairman of the symphony association's negotiating committee, Richard G. Kleindienst, that their position had not changed. We are still faced with a situation where the board of directors, who have made substantial commitments to improving the quality and stature of the orchestra, are refusing to make a commitment to the current orchestra members and to the future of the National Symphony."

At the same time that the negotiations were in progress, the symphony association was holding its annual meeting. David Lloyd Kreeger, retiring after eight years as president, spoke "with deep regret" of "leaving office at this unhappy time." There was no other mention of the strike.Kreeger is being succeeded by Austin Kiplinger of Kiplinger Letters. The symphony management issued no statement following the breakdown of negotiations.

The musicians are continuing their picket lines at the Kennedy Center.