Local farmer Moha Saleh said 27 people, including women and children, were also injured in the attack, which began when the Islamist militants stormed the village at around 1:00 am.
"They also set many houses ablaze after accusing us of telling soldiers their whereabouts,"
Local resident Goni Musa, a vigilante who fights against Boko Haram alongside the Nigerian military, gave the same death toll.
"They burnt down houses and shops before they left, yelling 'Allahu Akbar'. Our terrorised women and children fled into the bush and returned to Maiduguri this morning," he added.
Maiduguri, the biggest town in northeast Nigeria, is some 20 kilometres (12 miles) north of Malari.
"This morning 13 bodies were recovered, some had been shot in the back, which means they were fleeing when the terrorists killed them," Musa said.
State police commissioner Aderemi Opadokun confirmed the attack but gave a lower toll.
"The attackers burnt down some houses and killed seven persons in the village situated along Konduga-Maiduguri road," Opadokun told reporters in Maiduguri.
Malari has been the target of numerous attacks in recent months, including a suicide bombing by a youth in a mosque in the middle of the Muslim holy month of Ramadan in July which left 12 people dead.
The group's bloody insurgency in Nigeria alone has left more than 15,000 people dead since 2009. In recent months, the group has increasingly expanded its operations into neighboring countries.
Boko Haram was also accused of attacking the town of Gamboru on Saturday, near the border with Cameroon.
Witnesses in nearby villages said the militants had set fire to houses, sending columns of black smoke into the sky.
Umar Babakalli, a refugee from Gamboru who fled to the nearby Cameroonian town of Fotokol several months ago, said he saw fighter jets circling overhead "but there was no sign of any bombardment".
It was not immediately clear if the fires had caused any victims but Babakalli said Gamboru, a town which has faced repeated Boko Haram assaults, was deserted. "There is nobody in Gamboru," he told AFP.
Earlier on Sunday, the Nigerian army said it had carried out air strikes in the northeast to repel an attack by Boko Haram and had killed a "large number" of the extremists.
The Nigerian Air Force said it had "successfully repelled an attack on Bita village by the Boko Haram terrorist group" in a combined operation with ground troops after spotting militants planning an assault.
The air raids came as Nigeria and its neighbors prepare to launch a new multinational force to combat Boko Haram, in the face of the group's escalating violence in the region.
The new 8,700-strong multinational force -- made up of troops from Nigeria as well as Cameroon, Chad and Niger -- is expected to go into action soon, officials say.
Nigerian President Muhammadu Buhari, who won an election in March on a promise to defeat the jihadists, said Friday the new force would "lead to the speedy defeat and elimination of Boko Haram"
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