At least one other officer was fired and several others were reprimanded for their handling of high-profile cases, the Phoenix police chief said.

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The Phoenix Police Department has fired an officer who drew his gun on an African-American family while responding to a shoplifting complaint, an incident captured on cellphone video that spread widely online and set off outrage nationally.

At least one other officer was terminated and several others were reprimanded for their handling of other high-profile cases, Chief Jeri Williams said at a news conference on Tuesday and in a Facebook post. The officers have the right to appeal the decision.

She said that in the first case, she had decided to fire Officer Chris Meyer for the way he responded to the shoplifting call on May 27, an episode that caused “adverse effects on both the Phoenix Police Department and our community.” Another officer who was involved in the case was given a written reprimand, she said.

Chief Williams also announced that 72 employees had been “flagged” for having possibly inappropriate social media posts. After an internal investigation, 11 employees were singled out for serious violations of policy, and one of them, Detective Dave Swick, was terminated, the chief said.

Nine others who had been singled out were suspended for eight to 40 hours, and the remaining employee was still being investigated, she said. The rest were given “supervisory coaching,” she said.

“Our officers’ behavior was unacceptable,” Chief Williams said. “I expect them to be respectful, professional and compassionate in every situation and every encounter.”

She said the disciplinary review board had recommended that Officer Meyer, who is white, receive a six-week unpaid suspension. “But the decision on discipline is mine,” she said, adding that she had met with him and considered the facts of the case. “I have notified him of my intention to terminate his employment,” she said. Like the other officers, he has the right to appeal.

The officer who received a written reprimand for the incident had tried at one point to “de-escalate” the situation, the chief noted.

In the May encounter, the Police Department said on Facebook, a manager at a Family Dollar store alerted an officer to a possible shoplifting incident and said that the people who did it were getting into a car. The department said officers had found the family’s car a mile from the store.

Two videos show officers yelling at the parents, Dravon Ames and Iesha Harper, who are accompanied by their two children. An officer can be heard saying that he is going to “put a cap” in Mr. Ames’s head. As Mr. Ames exits the vehicle, an officer presses him against the pavement and handcuffs him, then pushes him against a police vehicle.

Video shows another officer pointing his firearm toward the car as the couple’s 4-year-old daughter exits it from the back seat, followed by Ms. Harper, who is carrying her 1-year-old daughter in one arm. An officer yells at her to put the child on the ground and grabs her arm.

The police report portrays the parents as being slow to comply, yelling at officers and making movements that appeared as if they might have been reaching for weapons.

But the couple have said that is not true, stating that one of the officers pushed Mr. Ames’s head onto the hot pavement, threw his head against the car, kicked him in the leg so hard that he collapsed, and punched him in the back even though he was obeying their orders.

The couple said that the officers violated their civil rights, and their lawyer, Thomas C. Horne, a former Arizona state attorney general, filed a notice of claim — a precursor to a lawsuit — that said the couple had not realized until they were back at their car that their 4-year-old daughter had walked out of the store with a doll.

“We have a mediation meeting to try to settle on Dec. 18,” Mr. Horne said on Wednesday. “If we don’t settle, I will sue shortly after.”

As The New York Times reported in June, Mr. Horne said officers had been alerted by an “anonymous alleged witness” that the couple had been shoplifting, and had followed them without their patrol car sirens on. Once the car stopped, an officer approached the driver’s side with a gun drawn, Mr. Horne wrote, and then opened the door and began to shout at Mr. Ames.

A second officer pointed a gun at Ms. Harper, who was sitting in the back seat on the driver’s side and was “pregnant, which was obvious from her appearance,” Mr. Horne wrote.

The door to the car was malfunctioning and the couple could not get out of the car, the notice said. The officer walked around the car with his gun drawn and dragged Ms. Harper and her daughters out of the car by the neck, according to the notice.

The couple’s arrest was one of several instances in recent years in which the police in Phoenix have been accused of providing selective or misleading accounts of events. In 2018, the city had 44 police shootings, far more than any city of its size.

Chief Williams said that the department receives more than two million calls for service each year, and that the “overwhelming majority” of them end well.

“But when they don’t, we will deal with the misconduct and create a dynamic where further harm isn’t done,” she said.

Richard A. Oppel Jr. contributed reporting.

Christine Hauser is a reporter, covering national and foreign news. Her previous jobs in the newsroom include stints in Business covering financial markets and on the Metro Desk in the police bureau. @ChristineNYT