Talks between the National Basketball Association and the NBA Players Association broke off after 24 minutes yesterday in New York. The union formally notified the league it will strike April 2 unless a new labor contract is reached.

Yesterday's abbreviated meeting was the first since the players announced a strike deadline two weeks ago. No new talks were scheduled.

"No purpose was served under the circumstances to continue the meeting," Commissioner Larry O'Brien told the Associated Press. "It is depressing to me that this set of circumstances arises given the history of sports in this country and strikes in the last year."

The players have been without a collective bargaining agreement since June 1. Negotiations have been ongoing and the sides have basically agreed to a guaranteed compensation plan that would put a ceiling on salaries and give the players a percentage of the league's gross revenues. That figure would be between the 40 percent the league is offering and the 55 percent the players want.

The stumbling block has come over when the plan would go into effect. The league, which lost a reported $16 million last season, said it needs to adopt the plan immediately in order to survive. The players say they won't agree to it until after the 1986-87 season, when the 1976 Oscar Robertson suit settlement expires.

The Robertson settlement established the NBA's free agent system. Larry Fleisher, general counsel for the players association, said the players "won't agree to anything that will affect free agency until after the Robertson settlement expires."

The NBA has said at least 10 of its 23 teams are in financial trouble and the league as a whole is in jeopardy.

Said Fleisher: "They said that unless we agree to something that will relieve them of their financial problems, there is nothing to talk about. We told them that if that involves giving up free agency, we couldn't do that. That ended the meeting."

Representing the players at the meeting were Fleisher, Charles Grantham, executive vice president of the union, and Milwaukee center Bob Lanier, president of the NBAPA. The NBA's general counsel, assistant counsel and the outside attorneys attended.

Before the meeting, Bullets owner Abe Pollin, chairman of the NBA labor negotiating committee, said, "I am ready to continue negotiating, but I will not negotiate under the threat of a strike."

Monday, a special NBA committee announced that Utah, Cleveland, San Diego, Denver and Indiana are "problem franchises" and could be dissolved, merged or relocated at the end of the season. Denver President Carl Scheer denied his team was in financial difficulty yesterday, saying "there's absolutely no truth to it."