Hundreds of Islamist gunmen seized the town of Baga and neighboring villages, as well as a multinational military base last weekend.
Musa Bukar, chairman of Kukawa local government where Baga is located, claimed that more than 2,000 people were killed in the attacks, but he could not explain how he arrived at that toll.
Bodies of residents killed by the militants litter the bushes in the area, he said.
But the local chief of Baga, Baba Abba Hassan, who is now seeking refuge, rejected that claim.
He said hundreds of people might have been killed, but not 2,000. The actual toll will be known after a head count of households is completed.
"If reports that the town was largely razed to the ground and that hundreds or even as many as 2,000 civilians were killed are true, this marks a disturbing and bloody escalation of Boko Haram's ongoing onslaught against the civilian population," Amnesty International's Daniel Eyre said.
On Sunday, Baga resident Yusuf Maidaji told CNN that the Islamist militants torched hundreds of homes in Baga and looted shops.
"The toll could be huge because the gunmen opened indiscriminate fire on fleeing residents," said Maidaji.
Bukar said 20,000 displaced persons are camped in the city of Maiduguri, the capital of Borno state. Authorities are making arrangements to bring 10,000 others from the town of Monguno, 60 kilometers (36 miles) from Baga. Some residents fled into neighboring Cameroon.
Hassan said the militants went on a burning spree in recent days, setting homes deserted by residents in 16 villages they seized in the attacks.
Boko Haram has terrorized northern Nigeria regularly since 2009, attacking police, schools, churches and civilians, and bombing government buildings. It has also kidnapped schoolgirls.
The Islamist group -- considered one of the world's most deadly terrorist organizations -- has said its aim is to impose a stricter enforcement of Sharia law across Nigeria, which is split between a majority Muslim north and a mostly Christian south.