The move follows two recent jihadist attacks in which about 100 Malian soldiers were killed.
The offensive coincides with a similar move by French forces on the border regions of Mali, Niger and Burkina Faso.
"The defence and security forces of Mali have been engaged in recent days in a large scale offensive against terrorist bases in certain localities in the centre of the country," a statement said.
It said "several terrorists" had died, without giving a number and added that "vehicles and motorcycles had been burnt and identity papers of several nationalities were found" during the raids.
The government also denied jihadist claims on social media that they had seized armoured vehicles belonging to the army during recent attacks.
Mali's army has been struggling to contain the Islamist insurgency despite help from France, African neighbours and the United Nations.
Northern Mali fell into the hands of jihadists in 2012 before the militants were forced out by a French-led military intervention. But the jihadists have regrouped to carry out hit-and-run strikes in violence that has spread to central Mali.
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