NEW YORK — Negotiators for locked-out players and Major League Baseball bargained into the night for the second time in a week ahead of Commissioner Rob Manfred’s Tuesday deadline to reach a deal preserving a 162-game season.

Union chief negotiator Bruce Meyer and general counsel Ian Penny headed a bargaining team that met in the morning at MLB’s office across the street from Radio City Music Hall.

About three hours later, Deputy Commissioner Dan Halem, Executive Vice President Morgan Sword and Senior Vice President Pat Houlihan made the three-block walk for a 20-minute visit to the union’s office overlooking Rockefeller Center.

The sides continued speaking later in the day by telephone. As of around 8:30 p.m., the back and forth was expected to go on for at least several hours.

On the 97th day of baseball’s second-longest work stoppage, the sides appeared to be trading numbers on the key economic issues of the luxury tax, the amount of a new bonus pool for pre-arbitration-eligible players and minimum salaries.

It remained unclear whether this more intensive phase of talks could lead to an agreement or yet another breakdown in oft-strained talks that have dragged on for nearly a year.

About 16 1/2 hours of bargaining in Jupiter, Florida, that began Feb. 28 produced progress but led only to an angry breakdown in talks the following day, when Manfred announced the first two series for each team during the season had been canceled.

While it appears there is no chance opening day could take place as scheduled March 31, MLB told the union that Tuesday is the last possible day to reach an agreement that would allow a modified 162-game schedule, along with full salary and service time needed for free agency.

MLB on Tuesday offered a tax threshold starting at $230 million and rising to $242 million, a person familiar with the proposal said, confirming a move first reported by The Athletic. The person, speaking to The Associated Press on condition of anonymity because no public statements were authorized, said management’s proposal contained tougher penalties at a higher payroll level than in the expired agreement.