Among the dead was a senior Tuareg member, the government statement said.
The Tuareg fighters, allies of the Niger Movement for Justice (MNJ), said on its website that 26 soldiers died in two other separate clashes in the area, along with seven of its own fighters.
The government operation to recapture Tezirzait was announced by Niger's defence ministry following the release of four French hostages by the MNJ on Wednesday. The French were abducted on Sunday.
Both the Tuaregs and the MNJ demand greater autonomy for the West African region and a bigger share of its mineral wealth for local people.
Encouraged by rising world prices for uranium, the radioactive fuel for nuclear reactors, Niger hopes to become the world's 2nd largest uranium producer by 2011.