Police in eastern state claim killing 20 members of group behind recent deadly raid.
Government-backed troops scoured through forests in five districts of eastern Orissa for Maoist fighters on Monday.
The area is about 1,800km southeast of New Delhi.
TK Mishra, the home secretary of the Orissa state government, said: “We are hopeful of completing the operation very soon, but we’ll continue the operation till we get full success.”
Mishra said up to 20 fighters were killed since the group launched a wave of attacks on government targets last week.
At least 400 fighters took part in Friday’s attacks and stole roughly 1,000 weapons, Gopal Chander Nanda, the director-general of the state police, had said.
Orissa is one of India’s poorest states and part of an eastern swath of the country where the Maoists, who claim to be fighting for the rights of neglected tribal people and landless farmers, appear to be gaining ground.
The movement grew out of a peasant uprising in 1967 and has hit half of India’s 29 states.