The first attack on Monday afternoon killed 10 in the village of Shawa, some seven kilometres (4.3 miles) from Chibok, a number of residents told AFP on condition of anonymity.
Gunmen then stormed the nearby village of Alagarno late Tuesday and stole food, razed homes and fired on fleeing civilians.
"It was a sudden attack," said resident Haruna Bitrus, in an account supported by other locals.
"They began shooting and set fire to our homes. We had to flee to the bush. They killed 20 of our people," he added.
Many of those who fled the Alagarno attack ran to Chibok, where Boko Haram seized 276 schoolgirls on April 14.
The military said it had deployed heavily to the area to find the 223 girls who remain in captivity.
Major world powers including the United States are offering varying levels of assistance with the rescue mission.
Bitrus said that despite claims of a military build-up in the area, troops had not responded to the latest attack.
"While the gunmen were fleeing, three of their vehicles broke down and they have stayed behind to fix them. They were there up to this morning" with no response from the military, he said.
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