Mr. de Blasio called the eruption of violence “beneath the dignity of New York City.”

Now, it has the Police Department facing an “operational dilemma” in its laissez-faire handling of the demonstrators, a majority of whom are nonviolent, said Stephen P. Davis, the deputy police commissioner for public information. Top police commanders are set to meet on Monday.

“How do you allow the larger group to continue while at the same time prevent the instigators from getting what they want?” he said on Sunday. “Last night is going to have to require some re-evaluation of how we’re doing it.”

On Sunday, the police arrested a 29-year-old adjunct instructor at the City University of New York on felony charges in the assault of the two lieutenants during demonstrations on the bridge, which are protesting the police killings of Mr. Garner and other unarmed black men in New York and elsewhere.

The police said the man, Eric Linsker, had been at the center of a clash on the bridge Saturday evening as protesters began throwing objects from the walkway at the officers who were escorting a larger number of marchers in the roadway below.

The criminal complaint against Mr. Linsker identified one lieutenant as Philip Chan and the other by only his surname, Gallagher. The police said the lieutenants, members of the department’s Legal Bureau, saw Mr. Linsker trying to throw a trash bin over the side of the walkway and moved to arrest him. But a group of protesters stepped in and prevented the arrest, the police said. There were no other officers around to assist, the police said.