The Dallas Cowboys owner Jerry Jones, who this month said he would bench any of his players who “disrespect the flag” during the national anthem, says that the protest movement is damaging the NFL.

This season dozens of NFL players have knelt during the anthem to highlight racial injustice in the United States. The movement has split the nation, with many perceiving it as disrespectful to military veterans. The NFL’s television ratings are also down, although it is not clear whether this is directly linked to the protests, as TV sports audiences have fallen across America.

“There is no question the league is suffering negative effects from these protests,” Jones said on Sunday.

Jones’s Cowboys are valued at around $5bn, and he said he had heard from concerned sponsors. “Our ability to be substantive is based on having a strong NFL, a league that people are really interested in and want to watch and want to watch the games,” Jones said. “At all times, if I am anything, I am first and foremost a proponent of making the NFL strong. Making us have as many people watching the game as we can and watching in light of what we are doing and that’s playing football. If all this makes you stronger to represent messages, let’s don’t do it in a way that tears down the strength of the NFL.”

The Cowboys beat the San Francisco 49ers on Sunday. None of the Dallas players knelt during the anthem, although defensive end David Irving raised his fist at the end.

“I wouldn’t want to disrespect the anthem; wait until it’s over,” Irving told ESPN. “I’ve been asked that for the past three weeks, my statement is my statement,” Irving said. “That was a statement, nothing really to say about it. If you are in a position I am in or everyone else in this locker room is, you have to watch what you say, play things as smart as you can. I’m not going to speak on this, certain things are better off left unsaid.”

Seven 49ers players knelt on Sunday. Their former team-mate, Colin Kaepernick, started the anthem protest movement last season. He is currently without a team, a situation many believe is down to his decision to kneel, and the quarterback has filed a grievance alleging that NFL owners have colluded to keep him out of the league.