White House officials said no decision had been made. President Obama has the power to create national monuments, as he has done repeatedly during his two terms.

The push to create a national park or monument near the Stonewall Inn is intended to recognize the protests that erupted at the Manhattan bar after the police raided it in summer 1969. Those spontaneous protests by primarily gay men who frequented the bar are viewed by many as the beginning of the modern gay rights movement (though historians have noted the movement began before Stonewall).

The bar has been granted landmark status by the city, even as it continues to serve as a watering hole that caters not only to the area’s gay residents, but also to tourists from around the world, gay or straight.

“Stonewall deserves to be remembered,” said Brian Sullivan, a former bartender at the tavern who returns almost daily. “When I started coming here, gay people were disowned by their families, so this is the place where we formed a new gay family of our own.”

Mr. Sullivan, 57, leaned against the bar’s red-brick edifice as he recalled some of the history he had witnessed there, from harrowing police raids to resolute speeches by the drag queen Marsha P. Johnson.