After the prosecution briefly presented the charges, Presiding Judge Vladimir Vucinic said that Franjic's family was seeking 390,000 euros in damages, adding that the accused should pay the amount together.
The accused again pleaded not guilty to the charges, insisting they had nothing to do with the crime they were charged with.
According to the indictment, the accused prepared an explosive device that killed Pukanic and Franjic in Zagreb in October 2008 for a reward of at least 1.5 million euros.
The next hearing is expected on Friday.
In November 2010, a Zagreb court found six people, including Milovanovic, guilty of the murder of Pukanic and Franjic and sentenced them to prison terms ranging from 15 to 40 years.
Milovanovic was sentenced in his absence to 40 years in prison for setting off the explosive that killed Pukanic and Franjic in Nacional's car park in central Zagreb. Robert Matanic was sentenced to 33 years while his cousin Luka Matanic and their friend Amir Mafalani each received 16 years. Bojan Guduric got 30 years and Slobodan Djurovic was sentenced to 15 years because he had served as a liaison between the assassins and Sreten Jocic who had allegedly paid 1.5 million euros for Pukanic's assassination.