Trump and his surrogates have criticized the N.F.L. for allowing players to kneel or sit during the playing of the anthem. But Jones’s comments raised the possibility of a showdown between some of its most powerful owners and the players’ union.

Jones’s remarks were the most strident comments yet by an owner in the debate over the players’ right to protest during the anthem.

He made the comments after the Cowboys’ 35-31 loss to the Green Bay Packers on Sunday night. Jones was asked about Vice President Mike Pence, who attended an Indianapolis Colts game earlier in the day but walked out after about two dozen players with the visiting San Francisco 49ers knelt during the national anthem.

Pence later tweeted, “I left today’s Colts game because @POTUS and I will not dignify any event that disrespects our soldiers, our Flag, or our National Anthem,” referring to Trump. Pence, who flew from Las Vegas for the game and then traveled to Los Angeles later Sunday, was criticized for what many felt was a premeditated political stunt.

Jones has been the most vocal of the 32 owners in saying that his players should stand. After his team lost to the Packers on Sunday, he went much further.

Jones brushed aside a question about two Cowboys players who had raised their fists at the end of the anthem.

“But if there is anything that is disrespectful to the flag, then we will not play,” he told The Dallas Morning News. “You understand? If we are disrespecting the flag, then we won’t play. Period.”