They said many people were injured and some were missing after hundreds of Maoists raided a large government-run relief camp, where villagers shelter for security, in the state of Chhattisgarh early on Monday.
A police spokesman told Reuters by telephone: "This looks like a major planned attack. We are assessing the casualties. Dozens of houses [in the camp] have been burnt."
The camp is at Arabore in the Dantewada district, about 510km south of Raipur, the state capital. Police said those killed belonged to the Salwa Judum (Campaign For Peace), an anti-Maoist group set up by the state government.
Chhattisgarh is the worst-hit of 13 Indian states affected by Maoists who say that they are fighting for the country's India's impoverished peasants and landless labourers.
Groups of police officers in the state are being trained at a jungle warfare school established to counter the Maoist threat.