The delay was due to an eight-day national strike by lawyers, the ANSA news agency reported.
It comes a day before the separate trial of the ship's captain, Francesco Schettino, which is due to start in the Tuscan city of Grosseto. That trial is also likely to be delayed just after its start on Tuesday to another hearing on July 17th.
The Costa Concordia crashed into the Tuscan island of Giglio last year with 4,229 people from 70 countries on board on the first day of a Mediterranean cruise in a disaster in which 32 people lost their lives.
Schettino has been charged with multiple manslaughter, abandoning the ship before all the people on board were evacuated and for causing environmental
Four crew members including the ship's Indonesian helmsman, as well as the head of ship owner Costa Crociere's crisis unit, have agreed plea bargains with the prosecution for short prison sentences. The plea bargains now have to be ruled on by a court.