Hundreds of thousands of Nigerians fleeing Islamist militants are searching for sanctuary, say government and international relief officials, the latest fallout from Boko Haram's campaign to seize the northeast of Africa's most populous country.

Local authorities said Tuesday that in a fresh exodus from violence, hundreds of people continued to flee Gwoza, a town of about 50,000 near Nigeria's remote border with Cameroon that suspected Boko Haram fighters overran last Wednesday. Boko Haram has made the surrounding Borno state the epicenter of its insurrection against Nigerian soldiers, Christians and—increasingly—civilians who stand in its way.

"They are streaming over the hillsides," said Borno state Governor Kashim Shettima of the civilians who are trying to escape the violence.

Mr. Shettima said Nigerian officials and multinational agencies are sheltering 40,000 people in schools that had already closed because the insurgency had made them unsafe for students. In the past year, up to a million people have fled to the state capital of Maiduguri, he said, lodging with relatives and in tents at the city's limits.

The forced migration from Nigeria's violence is expected to strain everything from public services to food security, as a weak central government struggles to beat back the emboldened Islamist insurgency.