The refugees said they were compelled to return to Nigeria after Boko Haram last week attacked an island in Lake Chad.
The Nigerians said soldiers arrived at the fishing village of Lelewa and ordered them to leave. Niger officials did not immediately respond to request for comment.
On Monday, Niger said it was planning a military operation in the area to rout Boko Haram extremists and ordered its citizens to move further inland.
The agency's Charles Otegbabe, director of search and rescue, registered the new arrivals in Gaidam town, in the northeastern Borno state.
"We thought there would be about 2,000 but we have already registered more than 3,000 and there are still more people coming," he told The Associated Press.
The refugees said hundreds more were on their way. "They didn't even give us time to collect our clothes. We had to abandon everything," said Lubabatu Isa, a 21-year-old carrying a baby strapped to her back.
"There was no water. It was very hot. They collapsed and died. Nobody had any energy left to help them and we just had to leave them in the bush," said a distressed Auwal, 22. Niger is hosting more than 100,000 other Nigerian refugees who have fled Boko Haram and who apparently are being allowed to remain in camps outside the Lake Chad area.
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