A man went on a stabbing rampage in a small city in France on Saturday, killing one person and injuring several more in what President Emmanuel Macron called “an Islamist terrorist attack.”

“It was a terrorist attack, there’s no doubt — an Islamist terrorist attack,” he said, adding that the government was determined “to root out terrorism in our country.” The police said they were investigating the stabbing as a terrorist attack.

The man targeted a market in Mulhouse, a city about 70 miles south of Strasbourg, near France’s borders with Germany and Switzerland.

As he began his attack, the 37-year-old was heard shouting, “Allahu akbar,” according to France’s antiterrorism police. The Arabic phrase, meaning “God is great,” is an everyday expression used in religious and nonreligious settings alike, but has also become a war cry in some terrorist attacks by Islamic fundamentalists.

A civilian who tried to stop the man was killed, the police said. Three police officers were also injured in the attack, two of them seriously.

The man, who was arrested at the scene, has not been identified by name, but was on France’s terrorist watch list, Nicolas Heitz, Mulhouse’s prosecutor, told French media. He was registered on a list of persons the government is monitoring for potential radicalization who by law are obligated to leave French territory after the authorities have rejected their residence or asylum applications, according to Mr. Heitz.

“Horror has just swept over our city,” Michèle Lutz, Mulhouse’s mayor said in a post on Facebook.