Pemba — Peter N’Guila used to have no trouble supporting his family of three on his consultant’s salary. But since Islamic State-linked insurgents attacked a northern Mozambique gas hub town last month, he has seven more mouths to feed.

Hundreds fleeing continued hostilities in Palma have been pouring into Pemba, a port city about 250km to the south already bursting with those displaced by previous rounds of Islamist violence and a deadly cyclone in 2019...