The violent protests and unrest that spread across France after the fatal police shooting of a teenager last week diminished significantly overnight, the authorities said on Monday.

Still, as a reminder that tensions remain high, French mayors called for peaceful gatherings around the country to protest a spate of violent attacks on elected officials.

Nearly 160 people were arrested and three law enforcement officers were injured overnight, the Interior Ministry said on Monday morning, far fewer than in previous days, when as many as 1,300 people were taken into custody.

Fewer incidents were also reported across the country, after the authorities deployed 45,000 police officers and gendarmes for the third night in a row in an effort to bring the situation under control.

Nearly a week of violence was set off by the fatal police shooting of Nahel Merzouk, a 17-year-old of North African descent, during a traffic stop on Tuesday morning in Nanterre, a Paris suburb.

The officer who fired the shot has not been publicly identified. He was quickly placed under formal investigation on charges of voluntary homicide and detained.

The killing tapped into a deep-seated resentment toward the police, who have faced accusations of violence and discrimination, in particular by residents in some of France’s disenfranchised urban suburbs.

While many residents of those suburbs have said that they understood the anger that first sparked the unrest, they have also condemned the violence, which morphed from an initial outburst of rage concentrated in Nanterre and the Paris suburbs into a much broader wave of violence around the country.

French officials have said the violence was carried out by a minority that was motivated by something other than justice for Mr. Merzouk and broader concerns about their treatment at the hands of the authorities.

“When you loot a Foot Locker, a Lacoste store or a Sephora boutique, there is no political message,” Olivier Véran, the French government spokesman, said on Sunday.

Rioters have burned thousands of cars, attacked hundreds of buildings — including police stations, schools, businesses and town halls — looted supermarkets and stores, and clashed night after night for nearly a week with the police in cities around the country.

The average age of those arrested was 17, according to the French authorities, who have urged parents to keep their children home.

The Association of Mayors of France has called for peaceful gatherings at midday in front of town halls around the country to protest the violence. President Emmanuel Macron is also expected to meet on Tuesday with the mayors of over 200 municipalities hit by the unrest.

“We refuse to let our country continue to sink into chaos,” the association said in a statement.

A weekend attack on the personal home of Vincent Jeanbrun, the mayor of L’Haÿ-les-Roses, a small, usually quiet town in the southern suburbs of Paris that was also rocked by the unrest, resonated throughout the country.

In the early hours of Sunday, as Mr. Jeanbrun was monitoring the situation at his office, assailants rammed a car into his home with the intention of setting it on fire, according to local prosecutors, who have opened an attempted-murder investigation.

The mayor’s wife was forced to flee through the back garden with the couple’s children, injuring her leg in the process.

The French government and politicians from across the spectrum have rallied to support Mr. Jeanbrun, who told the TF1 news channel on Sunday night that, “I never imagined that my family would be threatened with death.”

Mr. Jeanbrun, who grew up in L’Haÿ-les-Roses and is serving a second term after being elected for the first time at age 29, said that a “handful” of rioters were discrediting a city of over 30,000 inhabitants.

“It’s out of the question for us to be victims, it’s out of the question for us to give up,” he said. “If we give in to fear, they win.”

One firefighter died overnight as he was battling a blaze that destroyed several cars in an underground parking lot in Saint-Denis, a northern suburb of Paris. The government said an investigation into the cause of his death was continuing, but the Paris Fire Department told local news media that the fire was unrelated to the unrest.