The two separate attacks targeted the Timbuktu boat on the Niger river and an army position at Bamba, in the northern Gao region with "a provisional toll of 49 civilians and 15 soldiers killed", according to a government statement.
It did not specify how many died in each assault, but the assaults were "claimed" by a group affiliated to al-Qaeda*.
Earlier the Malian army said on social media that the boat was attacked around 11:00 GMT by "armed terrorist groups".
The vessel was immobilized on the river and the army are evacuating passengers, a Comanav official said, speaking on condition of anonymity.
Images on social media showed a cloud of black smoke rising above the river. The incident took place in a remote area and the images could not be verified independently.
The attack comes after an al-Qaeda-linked alliance, the Support Group for Islam and Muslims (GSIM), announced last month that it was blockading Timbuktu, the historic crossroads city of northern Mali.
The impoverished state has been struggling with insecurity since 2012, when a revolt led by ethnic Tuaregs erupted in the troubled north.
The insurgency was fanned by jihadists, who three years later took their own campaign into central Mali, Niger and Burkina Faso, sending shockwaves across the Sahel.
However, the fragile deal came under strain after the civilian government was toppled in 2020 and replaced by a coup leadership.
Tensions in the region have revived in recent weeks after the UN peacekeeping mission in Mali, which has been told to leave by year's end, handed over two bases near Timbuktu to the armed forces.
The handover triggered clashes between the army and the jihadists and led to an angry showdown with the former rebels, stoking fears for the 2015 peace agreement.
*Terrorist organization banned in Russia and many other countries