Mediated talks between representatives of the NFL and its locked-out players recessed Tuesday and are not scheduled to resume until next month.

The talks with Chief Magistrate Judge Arthur J. Boylan, the mediator appointed by U.S. District Judge Susan Richard Nelson, are scheduled to resume on June 7, four days after a hearing before a federal appellate court in St. Louis. The U.S. Court of Appeals for the Eighth Circuit will consider Nelson’s ruling last month that briefly lifted the NFL lockout.

That ruling by Nelson has been put on hold by the appeals court. A three-judge panel of that court on Monday blocked Nelson’s decision, enabling the league to keep the lockout in effect through the appeal process.

Now talks between the league and the players are on hold as well. The two sides met for a second straight day in Minneapolis with Boylan Tuesday. NFL Commissioner Roger Goodell and DeMaurice Smith, the executive director of the dissolved players’ union, met with Boylan over lunch. But there were no indications of significant movement in the talks.

The league and players had four days of joint meetings with Boylan last month before the talks recessed until Monday.

In addition to the June 3 hearing, the league and players are awaiting a ruling by U.S. District Judge David S. Doty on possible damages in a case involving the NFL’s television contracts.

The players are seeking $640 million in compensatory damages from the league’s franchise owners and another $1.92 billion in punitive damages. They also are asking Doty to deny the league access to approximately $4 billion in annual TV revenue if the lockout extends into the upcoming season.

The league has asked Doty to give the players only the $6.9 million in damages they previously were awarded by the sport’s special master, Stephen B. Burbank.

Doty agreed with players in a March ruling that the league had structured its TV contracts improperly to provide owners with what would amount to a $4 billion lockout fund, leaving money on the table that would have been shared by players. League officials denied that allegation, calling the language in the contracts standard and saying that any money paid by the networks to the NFL during a work stoppage would have to be repaid in the future.