It is clear from interviews with N.F.L. officials and more than a dozen teams that owners and team executives would prefer that the protests end, both for personal reasons and because it risks inflaming the president, who has been a friend and ally of many of the owners, and alienating fans and sponsors. But they are also wary of appearing heavy handed and upsetting the image of unity that the league sought to project last weekend.

What has emerged in meetings across the league this week — from locker rooms to N.F.L. headquarters — is a strategy of not pushing back at an unpredictable president. Instead, the players, with input from team officials, are seeking to shape a message that shows their desire to stand together while still addressing the original intent of the protests: raising awareness of police brutality against African Americans and racism in general.

“The players have a right to speak their minds, but on the other hand, it can make it difficult because there isn’t anyone in America who doesn’t want to honor America,” Arthur Blank, the owner of the Atlanta Falcons, said in an interview. “You talk to other owners and the commissioner, they feel the same way, they support the players.”