Thakur said eight police died on the spot in the ambush and two more on the way to hospital, while five of the wounded were evacuated by helicopter.
Maoist rebels in India killed 10 police after luring them into a hilly, forested area sewn with booby traps and setting off the bombs, officials said on Tuesday, in what was one of the deadliest attacks this year.
Members of an elite police unit were acting on a tip-off that a group of rebels had gathered at the top of a hill in the remote south of Bihar state when they found themselves trapped at lower ground late on Monday, the state's director general of police, P.K. Thakur, said.
The Maoists triggered improvised explosive devices among a group of 25 stranded policemen, before the police killed three insurgents in a gun battle that lasted into the night, Thakur told Reuters.
"The police party had almost 100 troops. The first group got trapped in an area of land mines and there were serial blasts. The terrain is very difficult there and the extremists were on higher ground," Thakur said.
Maoist insurgents seeking the violent overthrow of the Indian state have been fighting for decades, launching hit-and-run attacks against security forces from jungle camps across swathes of poor and rural central and eastern India.
Thakur said eight police died on the spot in the ambush and two more on the way to hospital, while five of the wounded were evacuated by helicopter. The attack took place a few kilometres from Bihar's southern border with Jharkhand state.
The number of attacks has fallen in recent years but the Maoists, who say they are fighting to free the poor and landless from exploitation of their land, continue to enjoy some support among the poor and violence remains common.
According to the South Asia Terrorism Portal, left-wing extremist violence has left 236 people dead this year, almost the same as for the whole of 2015. Almost half of the dead have been killed in mineral-rich Chhattisgarh state.