Nuon Chea, 87, and Khieu Samphan, 82, are charged with crimes against humanity for their roles in the Khmer Rouge regime from 1975-1979.
Spokesman Lars Olsen said this was "the final milestone" before the verdict, which is expected some time next year.
It is believed that up to two million people died under the Khmer Rouge.
Lawyers of "civil parties", which represent the plaintiffs, gave their initial statements on Wednesday.
One of the lawyers, Pich Ang, described the Khmer Rouge as "one of the most heinous regimes history has ever known".
"This is the final milestone before the verdict," Mr Olsen told the Agence-France Presse news agency. "It is the last chance to convince the judges about the case."
Both Nuon Chea, the regime's number two leader, and Khieu Samphan, its head of state, have said in the past that they believed they were acting in the best interests of the nation and had been unaware of the full extent of killings.
Two other people also faced charges along with Nuon Chea and Khieu Samphan.
But Ieng Thirith, 80, formerly the social affairs minister, was released after the tribunal ruled that she was unfit to stand trial due to illness.
Her husband, former senior Khmer Rouge leader Ieng Sary, who served as the regime's foreign minister, died while on trial at the age of 87.
Khmer Rouge leader Pol Pot died in 1998.
The tribunal, established in 2006, has only sentenced one defendant so far. Chief jailer Kaing Guek Eav, known as Duch, was sentenced to life imprisonment for his role in running the notorious Tuol Sleng prison, where thousands of inmates were killed.
The tribunal has run into problems, including court workers going on strike over unpaid wages in September.
Rights groups and campaigners have criticised the pace of the trial and voiced fears that the age of its remaining two defendants may mean that justice is not served.
The UN-backed war crimes tribunal in Cambodia has started hearing closing statements, in what officials say is a crucial phase of the trial.