The fighting took place in Bosso, a Niger village near the border with Nigeria.
The government forces did not suffer any fatalities, Chad's army said in a statement.
Casualty figures are often hard to independently verify. However, a humanitarian source confirmed the losses saying 40 to 47 Boko Haram militants had been killed in Bosso and its surroundings.
The rebels were pushed back to Nigeria, and at least four Boko Haram vehicles -- one of them armoured -- were also destroyed, a Chad military source said.
The Nigerian army, however, says that Malam Fatori is under its control.
The private radio station Anfani, based in the city of Diffa in southeastern Niger also close to the border with Nigeria, reported "heavy aerial bombing" on Monday, mainly around Bosso and Malam Fatori.
Another Chad and Niger army operation on Sunday in Talagam -- a small town situated between Damasak, a town that was recaptured from the Islamic insurgents, and Malam Fatori -- led to the deaths of 54 Boko Haram fighters, Chad's military said.
A humanitarian organisation source reported the deaths of three Chadian soldiers after the fighting on Sunday.
Thousands of soldiers from Niger and Chad have been stationed for nearly three months in southeastern Niger. They launched an offensive in early March across the border into northeastern Nigeria, parts of which are a stronghold of the Islamic insurgents.
"The situation is totally under control" in Niger, said former foreign minister Mohamed Bazoum, who is close to the country's president Mahamadou Issoufou.
"The risk of attacks taking place are very low due to the elimination of all potential players," said Bazoum.
More than 13,000 people have been killed and some 1.5 million made homeless since Boko Haram launched its bloody insurgency in 2009.
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