Eyewitnesses said that the victims were killed when 10 terrorists on motorbikes stormed the village on Thursday, June 8.
Residents told the news agency on Friday, June 9, that the victims were killed when 10 terrorists on motorbikes stormed the village on Thursday.
They also kidnapped six others, the report said.
"They asked people to assemble but everyone started running towards the bush," a local resident, Usman Buba, said.
He said, "they seized six people in the confusion and slaughtered four while two managed to escape."
The attack came a day after soldiers arrested Boko Haram commander Adamu Rugurugu during a village raid.
Buba said the jihadists who attacked Hambagda on Thursday afternoon decided to slit their victims' throats instead of shooting them to avoid attracting the attention of troops stationed in Gwoza, two kilometres (1.2 miles) away, the report said.
"The attack was evidently in reprisal for the arrest of a Boko Haram kingpin who has been terrorising the village," the resident said.
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Another resident, Dahiru Alkali, confirmed Buba's account, adding that villagers had complained to soldiers of incessant attacks by Rugurugu and his men.
The terror group seized Gwoza in July 2014 and made it their headquarters.
Troops retook the town in March 2015 but Boko Haram have continued to raid nearby villages from their hideouts in the mountains along the border with Cameroon, despite government's declaration of victory over the sect.