A Chadian officer, who asked not to be named, said about 10 Chadian soldiers were killed and 20 wounded in fighting for the towns. Two sources with Niger’s military told Reuters five of its soldiers were killed in the clashes.
There was no official comment from the armies of either Chad or Niger.
“We have kicked the enemy out of these areas and they are now under our control,” a Niger military officer said.
The advancing troops had seized large quantities of arms and ammunition as well as vehicles, he said, and were undertaking a clean-up operation in the area. “The troops have taken dozens of Boko Haram elements prisoner,” he added.
Damasak, the town furthest into Nigeria, is 10 km (6 miles) south of the Niger border, where Nigerien and Chadian troops had been massing in recent weeks before the offensive.
A medical source in Diffa, the capital of the Niger region which borders Boko Haram’s heartland in northeastern Nigeria, said 30 wounded soldiers had been admitted to the town’s hospital.
A second Niger military source said about 300 Boko Haram militants had been killed. There was no official confirmation of the toll and it was not possible to verify the figure.
“We had permission from Nigeria for this action,” the source said.
There was no immediate comment from Nigeria, which has launched its own offensive against the militants. Their gains forced Nigeria to delay elections that were due in February.
Boko Haram’s six-year insurgency, which aims to carve out a caliphate in Nigeria’s northeast, has killed thousands. The group has pledged allegiance to Islamic State, which rules a self-declared caliphate in parts of Iraq and Syria, according to an audio clip posted online on Saturday.
Cameroon, Chad, Niger and Benin have mobilised forces this year to help Nigeria defeat the group after it seized large amounts of territory and staged cross-border attacks.
Nigeria and its neighbours have been working to pull together plans and rules of engagement for a regional force of 8,700 troops but cooperation between the region’s armies has been strained at times.