“Watching the entire Eagles community come together has been an inspiration,” the statement said.

Some Eagles players addressed the issue more directly, disputing parts of the president’s statement. Torrey Smith, a former wide receiver for the Eagles, lashed out at Mr. Trump in a tweet shortly after the statement was released.

“So many lies,” Mr. Smith wrote. “Here are some facts 1. Not many people were going to go 2. No one refused to go simply because Trump ‘insists’ folks stand for the anthem 3. The President continues to spread the false narrative that players are anti military.”

In a statement late Monday, Mayor Jim Kenney of Philadelphia said that disinviting the Eagles “from the White House only proves that our president is not a true patriot, but a fragile egomaniac obsessed with crowd size and afraid of the embarrassment of throwing a party to which no one wants to attend.”

“City Hall is always open for a celebration,” he added.

It is not unprecedented for some athletes to skip White House celebrations of their victories, sometimes for political reasons. A handful of New England Patriots players skipped the celebration in 2017. Larry Bird, the famous Boston Celtics player, skipped a visit with Ronald Reagan in 1984. Michael Jordan, of the Chicago Bulls, did not participate in a White House celebration with President George Bush in 1991, reportedly citing scheduling issues.

But rarely — if ever — has a dispute between sports figures and a president escalated so quickly, and so spectacularly.

The clash between the Eagles and the president is the culmination of a cultural controversy that Mr. Trump inflamed last September when he attacked the former San Francisco 49ers quarterback Colin Kaepernick for kneeling during the national anthem in protest of police brutality toward African-Americans.

“Wouldn’t you love to see one of these N.F.L. owners, when somebody disrespects our flag, to say, ‘Get that son of a bitch off the field right now. Out! He’s fired. He’s fired!’” the president said at an Alabama rally.