The attack took place on Friday night at a house in Bamungaon village. The dead were identified as Kishori Shah (65) and his son Rajesh Shah (35), the police said.
Hundreds of people in Philobari area came out to the streets to condemn the attack on "Hindi speaking" community and blamed police for their failure to protect the lives of innocent civilians.
"The Hindi speaking community in Assam has been facing attacks since 2000. However, the state government has not done anything to protect the lives of the people living in Tinsukia and other districts for generations and assimilated with the locals," a demonstrator said.
The locals demanded Home Minister Rajnath Singh and Chief Minister Sarbananda Sonowal to visit Philobari and ensure security of the people.
They have also complained that the police were aware of a probable attack by the militants in the area but did not deploy adequate forces.
Tinsukia Superintendent of Police Mugdhajyoti Dev Mahanta said operations were launched against the militants and that security in the districts was intensified.