But Mr. Kerry has not specifically raised the question of human rights abuses during the latest offensive, and for a good reason: it is difficult to get a clear idea of what is happening. Since its start, much of northern Nigeria has been under a communications blackout, as cellphone service has been cut, physical access has been limited and information restricted to a series of military communiqués. They have announced the “capture and destruction” of Boko Haram camps, the deaths of “high-profile” Boko Haram members and other “terrorists,” the “disarray” of militants, the discovery and destruction of weapons caches, and the “securing” of various towns and settlements in the north from Boko Haram.

Nigerian military spokesmen have been at pains to deny any misconduct against civilians during the campaign, trying to reassure the country’s allies by announcing that they were pleased soldiers were sticking to what they called “the rules of engagement.” A spokesman did not respond Friday to a request for comment on the refugees’ accounts.

But some of the refugees who have massed here in this remote border village at the far eastern edge of Niger — there are at least 5,000 of them, and possibly as many as 10,000 in the area, officials say — described the fighting in terms that varied widely from the military communiqués.

Their testimony is among the first independent accounts of the Nigerian military’s offensive, and they spoke of indiscriminate bombing and shooting, unexplained civilian deaths, nighttime roundups of young men by security forces. All spoke of a climate of terror that had pushed them, in the thousands, to flee for miles through the harsh and baking semidesert, sometimes on foot, to Niger. A few blamed Boko Haram — a shadowy, rarely glimpsed presence for most residents — for the violence. But the overwhelming majority blamed the military, saying they had fled their country because of it.

They had come from multiple villages in Nigeria to one of the poorest nations on earth, overwhelming local officials. But at least here, they said, the soldiers of the Republic of Niger are drowsing under a giant tree at the border, not pointing their guns at the civilians who continue to cross it.

“The military just opens fire and kills people, and throws bombs and kills people, for no reason,” said Abubakar Ali, a shoe salesman waiting in one of the registration lines. “That is why you see these people here,” he said, pointing out at the crowd. “That is what is happening now in Nigeria.”