Three women suicide bombers entered the market last evening posing as buyers, then went to the nearby camp for people displaced by Nigeria's conflict and simultaneously blew themselves up. They all detonated their explosives nearly simultaneously, he said.
At least 30 people have been killed and some 80 more wounded in a bombing attack in Nigeria's northeastern state of Borno.
"Our village is right at the entrance into Konduga town and that is where both the camp and the makeshift market are situated, which made us an instant target point of the insurgents", said Kalli, the village chief.
An emergency source who spoke on condition of anonymity said that dozens of people were killed and others injured.
The attack - the latest in a string of assaults in the troubled region - took place in the town of Mandarari, 25 kilometres (15 miles) from Maiduguri, the capital of Borno state, said Baba Kura, a member of a vigilante force set up to fight jihadists.
Kura added that after the first explosion, "people were trying to close their shops when two other female bombers triggered their explosives, causing most of the casualties".
Boko Haram has waged an eight-year-war to create an Islamic state in northeast Nigeria.
Last month, an oil prospecting team was captured by al Barnawi's group.
Abubakar Shekau is the current leader of the militant Islamist group Boko Haram, he was deputy to founder Mohammed Yusuf, who was killed by police in 2009 while in custody. Media houses were attacked in April 2012, leaving at least 8 people dead.
Ibrahim Liman, the head of a local anti-jihadist militia force, confirmed the details of the attack.