Militants armed with heavy weaponry and rocket launchers attacked soldiers and members of a government-backed militia in Monguno near Lake Chad, killing at least 20 soldiers.
Militants also entered Nganzai at about the same time on Saturday and killed more than 40 residents, according to the local sources.
They also burned down the United Nations' humanitarian hub and the local police station in the area.
Militants distributed letters to residents, warning them not to work with the military, white Christian westerners or other non-believers.
On Tuesday, militants entered a remote village in the Gubio district of Borno state on Tuesday, killing at least 81 people.
Islamic State West Africa Province (ISWAP) claimed the responsibility for the two Saturday attacks as well as the Gubio attack.
ILKHA