Some 22 troops were injured while nine other soldiers are missing, the army said late Monday, adding that the toll could still rise.
The army had blamed the attack on "terrorists" in an earlier announcement late Sunday, using the term it typically uses for jihadists.
It had said its troops had been repelling an attack by the Islamic State in the Greater Sahara (ISGS) group, affiliated with the Islamic State organization.
The previous death toll was four soldiers and two civilians.
The two civilians killed were local elected officials, their relatives told AFP.
The army said Monday it killed seven from the attacking side, "likely" from the ISGS group, adding that there was "an unknown number of dead and injured carried away by the attackers".
It also said the attack caused damage to vehicles and residents' homes.
Tessit is located on the Malian side of the so-called three-border area in a vast gold-rich region beyond state control.
Like the whole of the zone, Tessit is even more isolated during the rainy season when heavy rainfall blocks access.
Armed groups under the umbrella of Al-Qaeda aligned jihadists Jama'at Nasr al-Islam wal Muslimin, or JNIM, are fighting ISGS there.
Thousands of residents have fled the area, many heading to the town of Gao, some 150 kilometer away.
The Malian army, which has a military camp next to the town of Tessit, has frequently been attacked in the area.
UN peacekeepers and, until a few months ago, French soldiers from Operation Barkhane, have also been deployed there.