Jeffrey Lurie, owner of the Eagles, took a different view. Don’t pander to the president, he said, by clamping down on the players. Work with the players and tune out the noise. The president will do what he does regardless.

“We’ve got to be careful not to be baited by Trump or whomever else,” he said at the meeting. “We have to find a way to not be divided and not get baited.”

Most of the owners took the bait anyway. Not long after the meeting, everyone from Commissioner Roger Goodell on down said they preferred if the players stood for the anthem. Behind closed doors, they debated how to change the league’s policy to force, not suggest, that players stand.

The owners changed that policy in May, infuriating the players, including many who did not protest during the national anthem last season.

Right on cue, the president declared victory. Mr. Trump said he was pleased with the N.F.L.’s new policy, but said he did not think the players should even be staying in the locker room in protest. If a player is not standing for the national anthem, Mr. Trump said, “Maybe you shouldn’t be in the country.”

If the owners thought the problem would be solved by tweaking their policy, they were wrong. They should have known better, even without Mr. Lurie’s warning. (Mr. Lurie took his own advice: In a statement issued Monday night, the Eagles thanked their fans but never mentioned the president.)

Mr. Trump has been fighting the league since the 1980s when, as the owner of the New Jersey Generals of the short-lived U.S.F.L., he successfully sued the league for violating antitrust laws. The victory was hollow. The upstart league won $3 in damages and collapsed. Mr. Trump has tried to buy N.F.L. teams over the years, but has been spurned, though he does remain friends with several owners, most notably Robert K. Kraft of the New England Patriots. Things changed once he became president. He has attacked the league mercilessly, poking at Mr. Goodell and taking glee in the league’s television ratings falling. He even floated the idea of removing some of the league’s tax exemptions.