At least four soldiers, two civilians and five assailants were killed on Sunday in an attack in a strategic border zone between Mali, Burkina Faso and Niger, Mali's army said.
The army blamed the attack on "terrorists" in an announcement late Sunday, using the term it typically uses for jihadists.
Earlier, 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 organisation.
The army's death toll could be "much higher," an elected official told AFP, asking not to be named for security reasons.
The two civilians killed were local elected officials, their relatives told AFP.
Tessit is located on the Malian side of the so-called three-border area in a vast gold-rich region beyond state control.
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Armed groups under the umbrella of Al-Qaeda aligned jihadists Jama'at Nasr al-Islam wal Muslimin, or JNIM, are fighting ISGS there.
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.
Thousands of residents have fled the area, many heading to the town of Gao, some 150 kilometres (90 miles) away.
The Tessit area, like the whole of the so-called three-border zone, is even more isolated during the rainy season when heavy rainfall prevents passage.
In a separate attack Sunday morning, five police officers were killed in Sona, in the Koutiala area of southern Mali near the border with Burkina Faso.
On Friday, suspected jihadists killed about 12 civilians in central Mali with explosives planted in the bodies of slain civilians that relatives had come to collect.
Mali is struggling with a long jihadist insurgency that has claimed thousands of lives and forced hundreds of thousands from their homes.
Violence that began in the north has spread to the centre and south of the country, as well as to neighbouring Burkina Faso and Niger.