Two loud explosions and sustained gunfire were heard about 6am on Saturday near Mali's main military base Kati outside the capital Bamako, and soldiers were deployed to block off roads in the area, a Reuters witness said.
There was similar unrest at around the same time in the central town of Sevare and the town of Kidal and city of Gao in northern Mali.
"There's gunfire everywhere," a witness in Sevare said.
Mali is battling insurgencies by the West Africa affiliates of al-Qaeda and Islamic State.
It is also grappling with a much longer history of Tuareg-led rebellion in the north.
Mali's army said in a statement "terrorist" groups attacked several positions in the capital and elsewhere in the country, without specifying locations.
Fighting was ongoing and asked the population to remain calm, it said.
Mali's military leaders took power after coups in 2020 and 2021, vowing to restore security, but militants continue to stage frequent attacks on the army and civilians.
Mohamed Elmaouloud Ramadane, a spokesperson for the Azawad Liberation Front (FLA), a Tuareg-dominated rebel alliance, said on social media its forces had taken control of positions in Kidal and Gao.
Four security sources said the regional al Qaeda affiliate Jama'at Nusrat al-Islam wal-Muslimin (JNIM) was also involved in Saturday's attacks.
There was no immediate claim of responsibility from JNIM, which frequently stages attacks on military installations throughout much of Mali, or from Islamic State in the Sahel Province (ISSP).
Gunfire could also be heard early on Saturday near a military camp close to Bamako's airport that houses Russian mercenary forces, a resident said.
"We hear gunfire towards the military camp. It's not the airport itself, but the camp that secures the airport," said the resident, who spoke on condition of anonymity for safety reasons.
The government led by Assimi Goita has leaned on Russian mercenaries for security support while initially spurning defence co-operation with Western countries.
Recently it has pursued closer ties with the US.