MINNEAPOLIS — The NFL and its locked-out players wrapped up another round of court-ordered mediation Tuesday without any signs of a new agreement and the clock ticking on the 2011 season.

Officials and attorneys for both sides said they will return for more closed-door talks with U.S. Magistrate Judge Arthur Boylan on June 7, four days after a key appeals court hearing in St. Louis on the legality of the lockout.

NFL lead negotiator Jeff Pash and Hall of Famer Carl Eller both said the talks went well, but there was no indication of any significant progress toward a new collective bargaining agreement. Pash said he thought Boylan had done a good job of “pushing the parties,” but he said he doesn’t believe the dispute over the future of the $9 billion business will be settled in court.

“The only way we’re going to solve this is by sitting down together,” Pash said, echoing the NFL’s preference for traditional negotiations in a collective bargaining setting and adding: “We owe it to our game. We owe it to our fans. We owe it to each other, to the players and to the clubs, to sit down and negotiate.”

Said Pash: “I think we got some work done today, and we’re going to keep at it.”

They’ve been at it for a long time.

The two sides met for 16 days before talks fell apart March 11 and the lockout began. Boylan, who presided over four days of mediation last month and two more days this week, also had lunch with DeMaurice Smith, executive director of the NFL Players Association, and NFL Commissioner Roger Goodell.

The two sides are not scheduled to meet again until June, just a month before training camps typically begin and just eight weeks before the first preseason game on Aug. 8.