The attacks were the first incidents in the area since it was placed under a state of emergency last weekend by President Goodluck Jonathan in the wake of a heightened offensive by Islamist sect Boko Haram.
“There were two explosions in the Mairi area… this evening. The explosives were planted in a ditch and detonated when nobody was around,” Lieutenant Colonel Hassan Mohammed, spokesman for a special military taskforce in Maiduguri, said.
The blasts occurred not far from a customs barrack, but Mohammed denied the establishment was the target.
In Damaturu a bomb went off at a popular open air drinking spot where a locally-brewed gin is normally served in a suburb named Kandahar, according to a regular patron.
“There was a loud bang… which raised dust all over the place. This was followed by pandemonium as everybody took to their heels,” Henry Samuel said by phone from Damaturu.
“So I can’t say whether there were casualties or not because I ran off as soon as I heard the blast.”
A hospital source said bodies of two civilians shot in a separate incident were brought in from an area on the outskirts of Damaturu on Wednesday.
It was not cleared who shot them or why.
Security authorities in the city could not be immediately reached for comment.
President Jonathan at the weekend declared a state of emergency in parts of four northern states hard hit by attacks blamed on Boko Haram.
The decree included parts of Yobe, Borno, Niger and Plateau states.
Maiduguri is the capital of Borno state and Damaturu of Yobe state.