The National Football League said it would consider requiring all of its personnel to stand for the national anthem, a move that could defuse a dispute with President Donald Trump but create a showdown with players over their right to protest.

The decision to consider the change came after weeks of persistent criticism from the GOP president about players protesting during the anthem, including his call for fans to boycott games if the demonstrations continue. On Sunday, Vice President Mike Pence left an Indianapolis Colts game after members of the San Francisco 49ers took a knee during the anthem.

The controversy is “threatening to erode the unifying power of our game,” NFL Commissioner Roger Goodell said in a memo to league executives on Tuesday.

Mr. Goodell didn’t release details of a plan to address the issue, but he said the league believes that all players should stand for the anthem. He also said the league would suggest other ways it could support social-justice issues that players want to champion.

Any change to the NFL’s policy would mark an abrupt reversal after the league presented weeks ago a unified front in response to Mr. Trump’s criticism.