Chief O’Neill said officers had the demonstrators’ safety in mind at all times. “We want to minimize the chances of people getting hurt,” he said. “We have to keep that in mind as we go through.”

He noted that the marches were shifting more quickly than messages shared on the Internet.

“It’s very, very quick,” he said. “Very fluid. I’m not even sure if the social media stays up with them; the decision to ‘make a right,’ or ‘make a left,’ or ‘go straight.’ It happens pretty fast.”

Chief O’Neill said the protesters had not prevented ambulances or other official vehicles from responding to emergencies during the first two nights of demonstrations. No sick person, or civilian with a health emergency has been unable to get help, he said.

Roughly 100 people were arrested on Wednesday; more than 200 were arrested on Thursday. Most were charged with civil disobedience, the police said.

Gideon Orion Oliver, a lawyer who is a member of the National Lawyers Guild and has served as an official observer for the group at protests in New York for more than a decade, said it was too early to judge how the police and the mayor were handling the current wave of protests.

Mr. Oliver said he was worried by reports he heard on Thursday about “some instances of police being heavy-handed.”

He said these protests were different than others he had observed because those involved had been more successful at doing things like occupying bridges and tunnels. But, he added, unique forces were at work in this instance.

The specific motivation for these protests, he said, is a belief that the police are overly aggressive. That, he said, meant it would be easy for aggressive action by the police to backfire and inspire even more anger among the demonstrators.