PHOENIX — The police used gas and smoke canisters to disperse crowds numbering in the thousands on Tuesday night outside the Phoenix Convention Center as tempers flared around President Trump’s divisive speech at a campaign-style rally here.
Hundreds of people ran off, streaming into the surrounding streets, coughing and wiping tears from their eyes.
Police helicopters circled above downtown Phoenix after the speech, telling people to leave the area or face arrest. While tensions were high before and during the speech — the police tried to keep supporters and opponents of the president apart outside — they escalated afterward.
Jeri L. Williams, the chief of the Phoenix Police Department, said at a news conference late Tuesday night that officers were attacked with bottles, rocks, and tear gas, and that two officers were being treated for heat exhaustion at a hospital.
She disputed the suggestion that officers were overly aggressive, saying they responded with tear gas and so-called pepper balls, which emit pepper spray, only after they were assaulted.
But some witnesses said that events unfolded differently, with protesters throwing a water bottle or two in the direction of the police, before the police fired tear gas into the crowd.
Mayor Greg Stanton, who also spoke at the news conference, said that the police had attempted to allow people on the streets of downtown Phoenix to protest peacefully, and that there had been no serious injuries. But he added that officials were going to examine whether the approach by the police was necessary.
“There’s going to be an after-incident review,” Mr. Stanton said.
Four people were arrested in connection with the rally, including two people charged with assaulting police officers, the authorities said.
“The handling by the police of this peaceful protest was reprehensible,” said Jordan Lauterbach, 31, a bartender who drove from Flagstaff to join in the demonstrations against Mr. Trump. “I was gassed tonight for exercising my right to express my views. I was disgusted by that.”
At some points, tension between Trump supporters and opponents approached disaster.
After the rally, the driver of a Ford Ranger pickup enraged protesters by performing the Nazi salute in their direction. A scene of chaos ensued as protesters approached the truck and yelled at the driver and passengers. The driver then tried to speed away from the protesters, raising fears of a repeat of the car-related violence in Charlottesville, Va., earlier this month. Police officers intervened to stop the truck and have its occupants get out of the vehicle.
The tension had started hours earlier. Before Mr. Trump landed here, thousands of supporters and opponents gathered around the convention center. They shouted at one another, chanted slogans, hoisted placards and complained about the 108-degree heat. Some expressed worries that the event would set off the kind of deadly violence that broke out in Charlottesville, Va., this month.
Waving an American flag as he marched past supporters of Mr. Trump, Hugo Torres pointed to a list emblazoned on his shirt under the heading “Bad Hombres”: former Sheriff Joe Arpaio, Attorney General Jeff Sessions, the Ku Klux Klan and the 45th president of the United States.
Mr. Trump’s appearance touched nerves in a city that has been at the center of the debate over restricting immigration. Mr. Stanton, a Democrat, urged Mr. Trump to delay his trip in an op-ed in The Washington Post, writing that the president “may be looking to light a match.”
While the president delivered his speech inside the convention center downtown, tempers flared on the streets around the site. Arguments between his supporters and opponents escalated to shouting matches in numerous locations.
Still, many Trump supporters said they welcomed the visit as an opportunity to express their views. Tim Foley, an Army veteran who leads his own citizens’ border patrol in Arizona, showed his Glock handgun to a reporter, saying he and his comrades had come to Phoenix to “keep the peace.”
“Ignorance is fueling the opposition to Trump,” Mr. Foley, 57, said in an interview outside the convention center alongside other members of his Arizona Border Recon, which he calls a nongovernmental organization. (Critics call it a militia.) “We’re the last line of defense. No one wants another Charlottesville.”
The violence at a rally of white supremacists in Virginia this month, which left a 32-year-old woman dead — and Mr. Trump’s widely criticized responses to those events — had many in the city bracing for clashes. Police officers barricaded downtown streets and patrolled the area. Restaurants closed early, and hotels restricted access to their lobbies to guests carrying key cards.
“We have a president without any sense of morality,” said Jimmy Muñoz, 72, an Army veteran who showed up with his family to protest. “Trump loves to rile people up and appeal to their worst instincts. We’re here to show we’re better than that.”
Others, however, expressed glee about the event.
“I can’t describe a Trump rally other than they’re the most fun things to go to,” said Paula Rupnik, 59, a consultant for a physical wellness company. She said she wanted to show her support for Mr. Trump and Mr. Arpaio.
“Trump’s base here in Arizona loves Sheriff Joe,” she said.