The 80 people killed include 30 in Madagali, a town 150 kilometres southeast of Maiduguri, where a twin suicide bombing took place, witnesses said.
Danladi Buba said two women detonated at a market near a busy bus station at about 9 AM Brig Gen Victor Ezugwu, the officer commanding in northeast Adamawa State, confirmed the attack but said casualties have yet to be established.
At least 50 people were killed and the death toll could go higher.
The military said there were multiple attacks at four southwestern entry points to the city.
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In another blast, two girls blew themselves up in Buraburin neighbourhood, killing several people, according to civil servant Yunusa Abdullahi.
"We are under siege," Abdullahi said. "We don't know how many of these bombs or these female suicide bombers were sneaked into Maiduguri last night." He said some residents have found undetonated bombs.
Acting on information provided by a captured insurgent, Nigerian troops "intercepted and destroyed" 13 suicide bombers and arrested one female suicide bomber in repelling the attackers, Maj Gen Lamidi Adeosun, the commander prosecuting Nigeria's war against Boko Haram, told reporters.
Maiduguri, the city under attack, is the birthplace of Boko Haram, which emerged as a much more radical entity after Nigerian security forces launched an all-out assault on their compound in the city, killing 700 people in 2009.
A rocket-propelled grenade then exploded, setting alight grass-thatched huts, and a second woman blew herself up, according to Isa. Among those killed was the village chief and 10 of his children, according to residents Ahmed Bala and Umar Ibrahim.