By Shaila Dewan and Mike Baker, New York Times–

Demonstrations continued across the United States on Sunday as the nation braced for another grueling night of unrest over police shootings and the death of George Floyd, amid growing concern that aggressive law enforcement tactics intended to impose order were instead inflaming tensions.

Videos showed police officers in recent nights using batons, tear gas, pepper spray and rubber bullets on protesters, bystanders and journalists, often without warning or seemingly unprovoked. The footage, which has been shared widely online, highlighted the very complaints over police behavior that have drawn protests in at least 75 cities across the United States.

In Salt Lake City, officers in riot gear shoved a man with a cane to the ground.

In Brooklyn, two police S.U.V.s plowed into a crowd of protesters .

In Atlanta, police officers enforcing a curfew stopped two college students in a car, fired Tasers on them and dragged them out of the vehicle.

And in Minneapolis, where there have been six consecutive nights of protests and clashes, a video appeared to show officers yelling at people on their porches to get inside and then firing paint canisters at them. “Light them up,” one officer said.

As crowds began gathering again in cities on Sunday, President Trump resisted calls to address the tensions roiling the country. Instead he used Twitter to criticize local Democratic leaders for not doing more to control the protests.

Mayors and police chiefs spent the day explaining, defending and promising full investigations into the actions of officers seen on the disturbing videos.

“I didn’t like what I saw one bit. I did not want to ever see something like that,” said Mayor Bill de Blasio of New York, who also complimented the city’s police officers for generally showing a “tremendous amount of restraint.”

Military vehicles in recent nights have moved down city streets as phalanxes of officers in full riot gear fired clouds of noxious gas. Yet the show of force showed little sign that it would bring calm.

Instead, some people said, it was escalating tensions and serving as a reminder of the regular use of military equipment and tactics by local police forces.

Mass demonstrations are among the most difficult situations that the police have to manage. They must balance constitutional liberties with the safety of officers and the public. Crowds are unpredictable and, in recent days, sometimes hostile. Too much force can escalate the situation — but so can too little.

Not all protests have erupted in violence, with some police forces showing a more positive relationship with their communities. In Petersburg, Va., Chief Kenneth Miller and a handful of police officers appeared alongside protesters to show solidarity. In Newark, a city where half the population is black, protests were angry but nonviolent .

a group of people walking down the street: Police officers in riot gear at a protest in Minneapolis on Saturday.© Victor J. Blue for The New York Times Police officers in riot gear at a protest in Minneapolis on Saturday.

And in Oklahoma City on Sunday, as a crowd of marchers seemed to grow tense, officers with the sheriff’s department’s tactical team took a knee in a pose popularized by the former N.F.L. quarterback Colin Kaepernick. The protesters cheered.

In other places, there was open hostility, with chaotic scenes and constant videotaping among protesters increasing the scrutiny on the tactics used by the police.

In Seattle, a video taken on Friday showed officers detaining someone on the ground and repeatedly punching the person.

Dae Shik Kim Jr., who was in the area and shared the video on behalf of a friend who wanted to remain anonymous, said it was just one in a series of tactics that troubled him during the protests.

“The tone that we felt from the police is: This is their rally,” Mr. Kim said. “They are going to control it from the beginning. They are going to dictate what happens. It’s a very offensive type of approach.”

In one arrest, captured on video after a group of people had gone into a damaged retail store, one officer put a knee on the back of the arrestee’s neck. Mr. Floyd, the man whose death on May 25 inspired protests in Minneapolis that have spread across the country, died after an officer kept his knee on Mr. Floyd’s neck for close to nine minutes.

As onlookers in Seattle shouted at the officer to remove his knee, his partner reached over and pulled it away.

The Seattle Police Department has said that officers that day took action after being assaulted with rocks, bottles and other projectiles, and that all uses of force would undergo a high level of scrutiny.

Chief Erika Shields of the Atlanta Police Department condemned the actions of the officers who fired upon the college students with a Taser, saying the episode had only underscored the fear and wariness that people of color have of the police. The officers involved were fired.

“I know that we caused further fear to you in a space that’s already so fearful for so many African-Americans, and I am genuinely sorry,” Chief Shields said in a news conference on Sunday. “This is not who we are. This is not what we’re about.”

In Minneapolis, businesses have been burned and looted and the National Guard has been called in to help restore order. But a member of the City Council, Jeremiah Ellison, summed up the situation this way: The police started it.

“No one was looting anything in the first night of this protest, no one was lighting anything on fire on the first night of this protest, and yet the response from the police was incredibly brutal,” he said. “The original provocation to street violence was from our officers.”

On the day after Mr. Floyd died, Mr. Ellison gathered with others at the site where Mr. Floyd was detained and walked with them to a nearby police precinct, he said. The crowd was relatively peaceful, he said, but the officers sprayed tear gas. Once the marchers reached the precinct, tensions grew, but in Mr. Ellison’s view the police overreacted.

“One of the city’s employees has just murdered someone in the most brutal fashion,” he said, “and for you to then pretend like you’re the victim and you’re under siege, to fire mace and tear gas and rubber bullets in response to water bottles being thrown — you have at that point 100 percent antagonized the situation.”

Mr. Ellison said the decision could have been made at that point to allow the precinct to be vandalized — a practice known as “negotiated management,” allowing some illegal activity like blocking a highway or damaging property in order to prevent worse events like arson or physical attacks.

Instead, when the police abandoned the precinct two days later, allowing protesters to set it afire, it was too late, Mr. Ellison said: “What could have been a strategic containment of destruction on Day 1 became a victory on the battlefield by Day 3.”

Many people complained that police officers across the country treated the crowds protesting racist policing with far less respect than they did the right-wing demonstrations in recent weeks against public health lockdown orders.

Experts agreed, saying research shows that the police are more likely to respond with force when they are the subject of protest, and that they respond more aggressively toward younger crowds and people of color than they do toward white and older people.

“There’s deep resentment on the part of the police that so many people are angry at them, and they’re lashing out,” said Alex Vitale, a sociologist at Brooklyn College who studies the police response to protest and coordinates the Policing and Social Justice Project. “Look at what we saw — people sitting on their own stoops getting hit with pepper balls . Anyone who looks at them funny, they’re attacking them.”

Paul Schnell, the Minnesota Department of Corrections commissioner, who was assisting in the official response, later apologized for that incident, which actually involved paint canisters. “We do not want there to be collateral harm,” he said.

In many places, the police defended their tactics as necessary to deter crime. In Dallas, Chief U. Reneé Hall said pepper spray and tear gas were needed to disperse demonstrators who were vandalizing property. “We will not tolerate tearing up our cities, our communities,” she said, according to The Dallas Morning News .

But critics said the protest was “a simple march” and the response was unwarranted.

The militarization of the nation’s police departments in recent decades has been on full display. But such equipment and training, including armored personnel carriers and SWAT team training, have been heavily criticized for warping the relationship between the police and the communities they serve.

Jennifer Cobbina, a criminal justice professor at Michigan State University, has researched the response to the protests in Ferguson, Mo., after the death of Michael Brown at the hands of the police in 2014, and in Baltimore after the death of Freddie Gray in 2015.

In Baltimore, she said, the police gave people more space to protest for longer before cracking down on unrest, resulting in a more favorable view of the police and a better understanding of the challenges they face. But Ferguson, where the unrest refused to die down, was heavily militarized.

“It makes a lot of the residents feel like the police are coming in as an occupying force,” she said. “This only creates a greater divide. The harder the state comes at them, the harder they’ll come back.”

Ben Fenwick and Rick Rojas contributed reporting.