Khieu Samphan, the former head of state, and Nuon Chea, Pol Pot's deputy, are already on trial for war crimes and crimes against humanity.
The second trial includes a charge of genocide related to killings of Vietnamese and Cham Muslim minorities.
The cases are being tried separately to accelerate proceedings, because the defendants are elderly.
A verdict in the first case, meanwhile, is expected on 7 August. Prosecutors are seeking life sentences for the two former leaders.
The Khmer Rouge ruled Cambodia for four years, from 1975 to 1979. Up to two million people are thought to have died of starvation, overwork or by execution under the brutal Maoist regime.