The call for the strike for next Sunday and Monday was made in a recorded statement sent to the BBC.
A spokesman for the Communist Party of India (Maoist), calling himself Abhay, said the shutdown includes all schools and businesses but is intended mainly to paralyze rail and road traffic, the BBC said.
He claimed that Rao, 58 and also known as Kishenji, wasn't killed in a gun battle but murdered by security forces after being captured.
"Intelligence agencies and the security forces arrested Kishenji and killed him in cold blood after a day. They tried to show as if he was killed in an encounter," Abhay said.
Security forces issued few details of the fight with Rao, which they said happened in a remote area of the eastern state of West Bengal, and were cautious to acknowledge that they had killed the leader. They initially said they were "99 percent" sure the man they killed was Rao.
"We have recognized his AK47 assault rifle, the rest will follow," one official said.
But last weekend, his body was cremated at his native village of Peddapalli in the Telangana region of Andhra Pradesh state where Rao's elder brother lit the pyre.
The funeral was attended by political leaders sympathetic to rebel causes, including the formation of a separate Telangana state.
Maoist guerrillas, also known as Naxalites after the village of Naxalbari where the group started in the late 1960s, are active in what government officials call the Red Corridor -- the mineral-rich but remote and poor eastern states of West Bengal, Jharkhand, Bihar, Orissa, Chhattisgarh and northern parts or Andhra Pradesh.
The death of Rao is the latest success, the federal government in New Delhi said, since the launch in November 2009 of Operation Green Hunt. Up to 50,000 paramilitary forces and tens of thousands of civilian draftees have been stationed in so-called Naxal-infested areas to patrol the countryside.
The Maoists attempt to win the hearts and minds of the rural poor, who are often attracted to promises of a better life. Maoists demand more of the wealth from the natural resources be spread among the poor. Many of the landless general population support the Maoists against what they see as a central government neglecting their basic living, education and health needs.
However, Maoists and the many splinter groups often show disregard for civilians, sometimes deliberately targeting them in brutal attacks.
In May last year Maoist rebels killed 20 policemen and at least 20 civilians in the Dantewada district in the southern part of Chhattisgarh state. The bus in which the people were traveling hit a land mine planted in the road.
The Dantewada district was the scene of a previous deadly rebel attack when Maoists attacked four security force camps killing 75 government militia members.
The government and some rebel groups have been in contact for peace negotiations but armed confrontations continue.
The circumstances of Rao's death were challenged by a local popular poet and known Maoist ideologue P. Varavara Rao, a report by the Indo-Asian News Service said.
He said Rao was killed in a "staged encounter" and West Bengal chief minister Mamata Banerjee was responsible for the death.
"During the past 43 years I have seen a lot of dead bodies but none like this," Varavara Rao said. "They cut him, burnt him, then pumped bullets into him. There isn't a single part of his body without an injury."
Varavara Rao said police kept Rao in custody for 24 hours and tortured him.
Varavara Rao accompanied Rao's niece to identify the body and return it to his native village in Andhra Pradesh.