The first defendant, the former commander of the now dissolved special purposes unit known as the Red Berets, Milorad Ulemek Legija, said that the indictment was incorrect, pleading not guilty to the charges.
The second defendant, Zvezdan Jovanovic, a former member of the Red Berets, also denied the charges.
Judge Nata Mesarovic then read out a statement Jovanovic had given to the police, in which he admitted to shooting the prime minister and described the murder in detail.
"I personally killed Zoran Djindjic. I was not interested in money. I did it to prevent our people being handed over to The Hague," Jovanovic told the police after being arrested in an operation dubbed "The Sword".
The other accused were expected to enter their pleas later in the day.
Djindjic, Serbia's first democratically elected prime minister, was shot dead outside government headquarters in Belgrade on March 12, 2003. The trial started on December 22, 2003.