There was no immediate official confirmation of the figure, but the Islamist group has previously carried out mass kidnappings.
Boko Haram’s abduction last April of nearly 300 schoolgirls in Chibok, also in Borno, stirred international outrage and drew global attention to the group’s six-year insurgency.
“They took 506 young women and children (in Damasak). They killed about 50 of them before leaving,” a trader called Souleymane Ali told Reuters in the town. “We don’t know if they killed others after leaving, but they took the rest with them.”
Troops from Niger and Chad last week found the bodies of at least 70 people in an apparent execution site under a bridge leading out of Damasak, where the streets remain strewn with debris and burnt-out cars after the fighting.
Ali said his wife and three of his daughters were among those seized.
“Two of them were supposed to get married this year. (Boko Haram) said ‘They are slaves so we’re taking them because they belong to us’,” he said.
Mohamed Ousmane, another trader, said the militants took his two wives and three of their children.
A 40-year-old resident who gave her name as Fana said fighters had rounded up captives in the main mosque before taking them out of town. She said she saved her two children by hiding them in her house.
Boko Haram wants to carve out a caliphate in northern Nigeria. A sharp increase in violence forced a delay in planned elections last month in Africa’s most populous country.
Nigerian, Chadian and Niger forces have driven militants out of a string of towns in simultaneous offensives over the past month.
Military authorities say all but three of the 20 local government areas occupied at the beginning of the year have been freed.
Nigeria’s rearranged election is now due to take place on Saturday.
Niger troops distributed food on Tuesday to a handful of residents who remained in Damasak. A few others returned to check their houses but left for the bush again.
“We’ve seen the worst possible things you can imagine, so after a certain point there was no point in trying to leave,” he said. “They killed all our friends, our family members, so we just submitted ourselves to God.”
There were reports over the weekend that Nigerian soldiers abandoned Damasak to troops from Chad and Niger who had assumed the tag of foreign liberators.
Fear and lack of motivation were the reason behind the noticeable absence of Nigerian soldiers.