Maoists on Thursday killed one of the four Bihar policemen they abducted four days ago, following a decision by a jan adalat or kangaroo court, their spokesman said.
The fate of the remaining three will be decided by 10 am on Friday, the spokesperson told a local TV channel.
Sub-inspector Abhay Kumar Yadav was killed at around 4 pm, six hours after expiry of their second deadline of 10 am.
After killing Yadav, the Maoists said the fate of the remaining three policemen would be decided by 10 am Friday if the state government failed to initiate a dialogue or negotiate with them.
Avinash, a self-proclaimed Maoist spokesman, told a local TV news channel that Yadav was killed after a decision was taken in a jan adalat. "The Bihar government compelled us to kill Yadav as the second deadline expired," he said.
Avinash said that Yadav's body will be handed over by Thursday night.
Yadav's wife Rajni was staging a sit-in outside Bihar Chief Minister Nitish Kumar's residence.
The other three policemen are Rupesh Kumar Sinha, Lukas Gete and Ehsan Khan.
The Maoists have said the policemen would be killed unless eight jailed Maoist leaders were released.
The families of the policemen have been desperately pleading with Chief Minister Nitish Kumar for help.
Avinash said after the second deadline expired at 10 am, top leaders of the Communist Party of India-Maoist (CPI-Maoist) were informed about the decision to hold a jan adalat.
The guerrillas had earlier set a deadline of 4 pm on Wednesday. Avinash later told local Hindi news channels they had decided to extend it till Thursday in view of appeals by the family members of the abducted policemen.
The rebels had abducted the policemen in a six-hour gunfight in Lakhisarai district Sunday. The gunbattle left seven policemen dead and 10 injured. Maoists claimed the gunfight was in retaliation for the killing of their leader Azad and a journalist.
The Maoists have also warned the Bihar government of more violent attacks if the operations against Maoists were not immediately stopped.
The joint security forces have fanned out in the hilly terrains in Lakhisarai and its adjoining Jamui and Munger districts to rescue the policemen.
According to local TV channels that claim to be in touch with the Maoists, the condition of one abducted policeman, Rupesh Kumar Sinha, has deteriorated in captivity.
His mother, Manju Sinha, has fainted thrice in the last two days. She fell unconscious Wednesday also when she came to meet Nitish Kumar with a plea to get her son released.
After getting news of the killing, Bihar Chief Minister Nitish Kumar said his government is ready for talks with the Leftwing rebels.
"We have been ready for talks," Nitish Kumar said on the sidelines of a function in the state capital.
He also said the eight Maoists lodged in different jails in Bihar, whose release is being demanded by the Maoists, are being taken care of well, and he expected the rebels to mete the same treatment to the abducted policemen.
"We respect the human rights of any person arrested, because this is a democracy. We look after their health, and the Leftwing rebels are part of our society. We also expect the same treatment of our people (policemen) by the Maoists," he said.
"There should have been talks across the table...I appeal to everyone to come forward. To make one a prisoner and then haggle, is not good. After all, the policemen were doing their duty."