Moussa Ag Infahi, director of the national police, told The Associated Press that three of the assailants had been killed while a fourth escaped.
Gunfire rang out at the Campement Kangaba on the outskirts of Bamako, according to a security official with the U.N. mission known as MINUSMA. The official spoke on condition of anonymity because he was not authorized to speak to journalists.
"I heard gunfire coming from the camp and I saw people running out of the tourist site," said Modibo Diarra, who lives nearby. "I learned that it was a terrorist attack."
Malian soldiers succeeded in entering the site, according to Commandant Modibo Traore, a spokesman for the Malian special forces in the former French colony.
"The operation is ongoing and we estimate that there are between three and four assailants," he said.
The U.N. official said those at the resort when the attack began included people affiliated with the French military mission as well as the U.N.
The French president's office, the defense minister's office and the French military would not comment immediately on the attack or on media reports saying that French forces are intervening.
The French Foreign Ministry would not say whether any French citizens were hurt or otherwise involved in the attack in the West African country.
French military spokesman Col. Patrik Steiger said he had "strictly no information" about French military involvement in the incident in Bamako. He said there are no French troops based in Bamako, but about 2,000 French troops based in northern Mali fighting Islamic extremists.
France intervened in Mali in 2013 to oust Islamic extremists who had seized control of the major northern towns the year before. While the militants were officially ousted, they have continued to launch regular attacks on U.N. peacekeeping and Malian military sites.
Sunday's violence came about a week after the U.S. State Department warned of "possible future attacks on Western diplomatic missions, other locations in Bamako that Westerners frequent."
Religious extremism in Mali once was limited to northern areas, although in recent years the jihadists have spread violence farther south, including a devastating attack on the Radisson Blu hotel in Bamako in November 2015. That attack left 20 dead - six Malians and 14 foreigners.
Associated Press writer Angela Charlton in Paris contributed.