Gopal Chandra Nanda, Orissa’s director-general of police, said the fighters involved in the attacks had attempted to hide in thick forest about 200km away but had been tracked by police.
The deaths occurred in confrontations on Saturday.
Hundreds of Maoist cadres attacked Nayagarh, just 80km from the state capital Bhubaneswar, late on Friday, killing 14 police officers and wounding another 12.
At least 1,000 pistols were stolen during the raid.
The Maoists say regularly stage raids in parts of eastern and central India where they have a presence.
The Maoists are called Naxalites after Naxalbari, a village in West Bengal state where the movement was born in 1967.
The fighters draw many of their recruits from among tribal communities, which are often desperately poor and live in areas where the Indian government has little presence.
Manmoham Singh, the Indian prime minister, has declared the Maoist campaign as the biggest single threat to the country’s internal security.