Maoist rebels in eastern India Monday released three policemen held hostage, three days after the guerrillas killed another abducted officer, officials said.

The four men were taken captive in the state of Bihar on August 29 during a Maoist raid on security forces that left 10 policemen dead.

"I can confirm the release of the three abducted policemen early this morning," additional director general of Bihar police P.K. Thakur told AFP.

Bihar state chief minister Nitish Kumar, who came under severe criticism for his handling of the hostage drama, told reporters: "Finally it is over now and we are happy for that."

He denied any deals had been done with the rebels.

Celebrations broke out in the officers' home villages, with residents distributing sweets, setting off fire crackers and offering prayers of thanks.

"We were blindfolded early today and made to walk through hills and forests and finally they released us," one of the officers told reporters.

The Maoists had threatened to kill all of the hostages unless jailed rebels were freed and security forces withdrawn from areas in the state controlled by the guerrillas.

The body of the dead policeman was found on Friday in a remote forested district 150 kilometres (100 miles) from the Bihar state capital of Patna.

Authorities in New Delhi launched a major offensive last year to tackle the worsening insurgency, but since then the Maoists have hit back with repeated attacks on the police and paramilitary forces.

The movement feeds off land disputes, police brutality and corruption and is strongest in the poorest and most deprived areas of India, many of which are rich in natural resources.

More than 200 security force personnel died in encounters with the rebels in the first six months of this year.

India's junior home minister Ajay Maken told security experts in New Delhi on Monday that major new funding was being spent on upgrading police in states hit by insurgencies.