The ambiguity in the rule has made it difficult for the league to fine players who have either sat or knelt for the anthem, and the owners had discussed clarifying the wording to make standing for the anthem mandatory.

By leaving the rule alone, the league has chosen to avoid more internal strife with its players and to potentially weather more criticism from fans and President Trump, who has repeatedly ridiculed the league for not firing players who demonstrate during the anthem.

“We need to be above petty attacks from anybody, because racial and socioeconomic inequality has existed in this country for too long,” Jed York, the chief executive and co-owner of the San Francisco 49ers, said when asked about the president’s criticism of the league. “You got to block out the noise and go do your job, and that’s what we need to focus on.”

The meeting on Tuesday included the N.F.L.’s commissioner, Roger Goodell; the director of the players’ union, DeMaurice F. Smith; and 11 owners, including Robert K. Kraft of the New England Patriots and Arthur M. Blank of the Atlanta Falcons. They met for almost four hours with a dozen players, including Malcolm Jenkins of the Philadelphia Eagles, Eric Reid of the 49ers and Kenny Stills of the Dolphins, all of whom have protested during the anthem.

“We just talked about how the owners could come alongside us and we could, collectively, collaboratively, work together to actually create some change, real changes,” Jenkins said afterward, flanked by other players. “We feel a real responsibility to our country, to our communities, so we’re working through ways to really have long lasting, real change.”

Jenkins said there had been no discussion during the meeting about prohibiting players from kneeling during the national anthem; whether players continue to do so, he said, would be an individual decision.