Kraft said he plans to be in Israel through at least Thursday. If NFL commissioner Roger Goodell requests his presence to join negotiations, he would return to the United States.
"We're on the phone daily, e-mail daily, and if necessary I might have to leave early," Kraft told NECN's Alison King and another reporter.
"It's a high priority," Kraft said. "I made a commitment here, so we're going to finish the important things we're doing here. It's unfortunate; it was supposed to be settled by now. That's how we planned this trip. But when one makes a commitment one has to live up to the commitment."
Of the labor talks, Kraft said, "It's so important to so many people in America. It involves so many people whose jobs are tied to the NFL thriving. We're doing everything we can to try to get a deal consummated. I personally believe it's possible. ... It's always good to be talking. When you have differences of opinion, it's the only way you have a chance. I know from ownership side, we feel there is a deal to be made and we'd very much like to do it."