The attacks in Bam-Buratai, in Nigeria's Borno state, and in the Diffa region of Niger, happened on Saturday while there was another raid in Gulak, in Nigeria's Adamawa on Sunday.
Boko Haram hit-and-run raids -- once a trademark of the Islamic State group affiliate -- have declined in recent months in the face of a sustained Nigerian army counter-offensive in rural areas.
Instead, the group has increasingly favoured suicide and bomb attacks against civilians in towns and cities to secure maximum casualties and publicity.
The attackers were "shooting indiscriminately and throwing explosives into homes", said one local, who asked not to be identified, from the town of Biu, 20 kilometres away.
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"They shot dead three people and burnt another to death in his home before abducting two women and three children and driving them away in the two vehicles to they took from the village."
The remote farming village is near the home of Nigeria's chief of army staff, Lieutenant-General Tukur Buratai, which was itself targeted in September 2014 and 20 people were killed.
Across the border in Niger, a local official said four people were killed, two others injured and some 50 homes torched in a village near the provincial capital, Diffa, on Saturday evening.
"The Boko Haram members were armed with Kalashnikovs and came across the Komadougou Yobe" river that divides Niger and Nigeria, Fougou Boukar told state television.
State television showed hundreds of distressed villagers praying in memory of the victims. Some of them showed scores of empty cartridges they had gathered after the attack.