PARIS — French officials said on Tuesday that they would ban potentially violent protests in key areas like the Champs-Élysées in Paris, following a surge of violence during Yellow Vest demonstrations over the weekend that led to intense criticism of the government’s handling of security around tourist neighborhoods and wealthier areas.

Prime Minister Édouard Philippe said in a televised statement from Paris that after “intolerable” events over the weekend, the government had decided to ban any future Yellow Vest demonstrations “in the areas that have been most targeted,” if authorities became aware of “extremist elements” that intended to vandalize.

Mr. Philippe said one of those areas would be the Champs-Élysées, a major avenue in western Paris with luxury stores and tourist attractions that has become a focal point for the protests.

On Saturday, “breakers,” or casseurs, smashed an upscale restaurant, looted 27 stores and set kiosks and a bank on fire, forcing firefighters to evacuate a mother and her baby who were trapped on the building’s second floor.