At a rally on Friday in Huntsville, Ala., the president alluded to some of those factors, saying that the “No. 1 reason” ratings were down “massively” was that “they like watching what’s happening with yours truly.”

Mr. Trump first raised the protest issue at the Huntsville rally, where he also suggested that officials who penalize players for hitting too hard during games were “ruining the game.” On Saturday, in a series of early-morning tweets, the president pressed his N.F.L. criticism and took on top basketball players as well, saying he had disinvited the N.B.A. champion Golden State Warriors from a planned White House visit because of their star player Stephen Curry’s public opposition to him.

The fight has struck a chord with many of Mr. Trump’s core supporters, some of whom applauded him on social media for his stance. But it drew harsh denunciations from many prominent African-American players, including LeBron James, and an unusually strong rebuke from Roger Goodell, the commissioner of the N.F.L., whose owners include many donors to, and friends of, the president.

Mr. Trump struck back at Mr. Goodell on Saturday evening, nearly 12 hours after he had first raised the topic on Twitter, tweeting that the commissioner’s statement was “trying to justify the total disrespect certain players show to our country.”

“Tell them to stand!” Mr. Trump added.

Robert Kraft, the owner of the New England Patriots, who is a close friend of Mr. Trump’s and who has spent the night at the White House and ridden with him on Air Force One, issued a pointed statement on Sunday in which he said he was “deeply disappointed with the tone of the comments made by the president” at the rally, and defended players’ right to express themselves.

“Our players are intelligent, thoughtful, and care deeply about their community, and I support their right to peacefully effect social change and raise awareness in a manner they feel is most impactful,” Mr. Kraft said.

On Sunday, White House officials defended the president’s position, arguing that professional athletes had no business expressing their views on the field.