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The unified silent display during the "Star-Spangled Banner" came in the wake of team owner Bob McNair's controversial "inmates running the prison" comment, a league source told ESPN's Adam Schefter.
The Texans held a players' meeting Saturday in Seattle to decide how to handle Sunday after McNair's comments surfaced, the source said.
According to the source, the players discussed a variety of options including kneeling together, and also discussed peeling the Texans decal off of their helmets or raising their fists.
The players all held hands. Most kneeled or sat down, while at least one player appeared to remain standing.
McNair's comment was made during the owners meeting in New York earlier this month. Referring to ongoing player demonstrations during the anthem, he said, "We can't have the inmates running the prison."
It was featured in an ESPN The Magazine story published Friday that looked in detail on what went on at an Oct. 17 meeting of select NFL owners, players and union leaders and the full owners meeting the following day at which McNair made the comment.
McNair apologized for the comment Friday and again Saturday, saying: "I am truly sorry to the players for how this has impacted them and the perception that it has created of me, which could not be further from the truth."
On Saturday morning, he met with Texans players and expressed regret for the initial comment. One day earlier, Texans players considered a walkout from the team facility, and two players -- star wideout DeAndre Hopkins and backup running back D'Onta Foreman -- were listed as Did Not Practice-Not Injury Related on the injury report, absences that sources said were directly related to what McNair said.
Also Saturday, a coalition of NFL players extended an invitation to McNair, commissioner Roger Goodell and unsigned quarterback Colin Kaepernick to a Monday meeting in Philadelphia at which they hope to address players' "immediate concerns before additional progress can be made."
It was not immediately known if McNair, Goodell or Kaepernick would attend. A league spokesman had said earlier this week that Kaepernick was expected to be invited to the next meeting between NFL players and owners.