— The owners of the 32 NFL teams approved a new 10-year labor agreement with the players Thursday and decided to lift the sport’s four-month-old lockout – provided players approve the deal as well. The owners’ moves put the onus on the players to decide whether to put the league back in business.

Players will be permitted to begin reporting to teams’ training facilities for voluntary workouts beginning Saturday if the players’ executive committee recommends by then that all the players approve the collective bargaining agreement.

The free agent market would open Wednesday, contingent on the close to 2,000 NFL players approving the labor pact by then. Teams would open their training camps on the same day.

“It’s a good agreement,” said Jeff Pash, the lead labor negotiator for the league. “It’s a fair agreement.”

Player representatives spoke to DeMaurice Smith, the executive director of the NFL Players Association, in a conference call Thursday night, but did not vote on the agreement.

“As you know . . . issues that need to be collectively bargained remain open, other issues such as workers’ compensation, economic issues and end-of-deal terms remain unresolved,” Smith wrote in an e-mail to players. “There is no agreement between the NFL and the players at this time.”

Reaction from some players on Twitter and other media was highly critical of the owners’ decision. “Look guys I have no reason to lie! The truth of the matter is we got tricked, duped, led astray, hoodwinked, bamboozled! & I’m sorry you did too!” wrote Vonnie Holliday, the Redskins’ player representative, on his Twitter account.

More difficult to gauge was how rank-and-file NFL players will react now that the prospect of going back to work — and receiving their first paychecks for the 2011 season — is on the table.

Although the two sides still had differences on some side issues, there was broad agreement by both the league and the player representatives on the major components of a new collective bargaining agreement.

Under the owners’ proposal, teams would be allowed to begin re-signing their own free agents and signing their rookies to conditional contracts beginning Saturday. Those contracts would be voided if the players don’t approve the labor deal. Owners also approved a new system for revenue-sharing among the teams.

The deal also would resolve the litigation between the two sides, including the players’ antitrust lawsuit against the owners, a case filed by the players involving the sport’s television contracts, and a claim by the players of improper collusion by teams.

There were reports in recent days that the settlement of the lawsuit was being held up by the players’ side seeking the restoration of $320 million in lost benefits from last season, which was played without a salary cap, and asking for financial payments or free agency concessions for certain players who were among the named plaintiffs in the lawsuit.

But the resolution approved by the owners gave the players no lost benefits and no special concessions to the named plaintiffs in the antitrust case; it also made no payments to the players for the TV or collusion cases, people familiar with the situation said.

The players are to re-form their union as part of the deal. They dissolved the union the day before the lockout began and filed their antitrust lawsuit against the owners that day.

Smith and NFL Commissioner Roger Goodell spoke by telephone at least twice Thursday, people familiar with the deliberations said.

The collective bargaining agreement would be for 10 years, without any opt-out clauses, and would give the players just less than half the sport’s revenue, about 47 percent, under a salary cap system. It would set the salary cap for the upcoming season at approximately $120.4 million per team for players’ salaries, not counting an additional $22 million per club for players’ benefits. It would require teams to spend at least 89 percent of the annual salary cap in cash beginning in 2013, and it would include a rookie pay system to curb the amount of guaranteed money in rookies’ contracts.

The deal would keep the regular season at 16 games per team, shelving the 18-game season proposed by the league, and would reduce offseason workouts for players and limit hitting in some practices. The number of weeks of offseason workouts would be reduced from 14 to 10. The number of allowable organized team activities would be cut from 12 to nine, and there would be fewer full-contact practices in training camp and during the season.

It would restore the requirement for players with expired contracts to be eligible for unrestricted free agency to four seasons of NFL experience, down from the six seasons required last year in a season without a salary cap.

The agreement would not subject the sport’s labor situation to ongoing oversight by a federal court, a key provision for the owners. Disputes stemming from the labor deal instead would be settled by an arbitrator.

Players could appeal discipline by the commissioner in drug cases, but not in personal conduct cases, to an arbitrator, those people said. The drug-testing portions of the deal are not yet finished but it would be likely that blood-testing of players for human growth hormone would be included as proposed by the league, according to people familiar with the deliberations.

“This was a long, tough negotiation,” New York Giants co-owner John Mara said. “I can’t say we got everything we wanted out of this deal, and I think they would say the same thing. That usually means it’s a fair deal.”

Goodell said the league canceled the Aug. 7 preseason opener, the Hall of Fame Game scheduled to be played between the St. Louis Rams and Chicago Bears in Canton, Ohio.

“Time is too short” for that game to be played, Goodell said.

The remainder of the preseason would be played as scheduled, Goodell said. The regular season is scheduled to begin Sept. 8.

“There is an urgency to this,” Goodell said.

The NFL was scheduled to hold a seminar for team executives Friday in Atlanta to educate them on the deal that the owners approved.