One French citizen, one Belgian and three Malians were killed in the attack in the capital of Bamako, said Gabriel Toure, director of a local hospital.
An additional eight people were wounded, he said.
"Mali remains committed to seeking peace and will not be intimidated by those who have no other motives than to do away (with) the prospects of peace and harmony amongst the Malians," the government said in a statement.
A North African jihadist group, al-Murabitun, claimed responsibility for the attack, according to Mauritanian news agency Al Akhbar. The purported claim came in an audio message in which the group said it carried out the attack in retaliation for the killing of one of its leaders, Al Akhbar said.
"Al-Murabitun may be considered a regional competitor to al-Qaeda in the Islamic Maghreb (AQIM)," according to the Jamestown Foundation, a Washington-based research and analysis firm. The U.S. State Department said in January that al-Murabitun is a "newly-formed" militant group that has presence in northern Mali.
French Foreign Minister Laurent Fabius said the victim from his country was 31 years old.
French President Francois Hollande released a statement condemning the attack.
U.S. Secretary of State John Kerry expressed his condolences to the victims' families in a news conference in Paris on Saturday.
"This is an act of cowardice," he said. "But an act of opening fire in a restaurant filled with innocent civilians -- in the end, that only strengthens our resolve to fight terrorism in all of its forms, wherever it exists."
The French Embassy in Bamako warned its citizens to be on alert if they go out in public.
Though it's unclear whether any rebel group is responsible for the attack, Malian forces have battled Islamist militants in the northern part of the nation for years.
Fabius said the Malian government was interrogating some suspects.
Mali plunged into chaos after soldiers staged a coup three years ago. As a result, Tuareg fighters capitalized on the power vacuum to launch an insurgency that ended with their takeover of the north.
After the Tuareg fighters seized the region, a power struggle erupted with local Islamist radicals. The extremists toppled the tribe and seized control of a large piece of northern Mali, an area the size of France.
Since then, the nation has battled various rebel factions, mostly in the northern region, with the help of French and African forces.