Francesco Schettino is charged with involuntary manslaughter, causing a maritime disaster and personal injury to 150 people.
But Prosecutor Francesco Verusio objected to a plea deal and said the trial will go quickly, the Italian news agency ANSA reported.
"That Schettino is guilty, there is no doubt. The only thing left to determine is how long his sentence will be," Verusio said.
If convicted of all the charges, Schettino could face a sentence of 25 years in prison.
The Costa Concordia was carrying 3,200 passengers when it turned on its side after striking rocks off the Italian island of Giglio in January 2012.
CNN said the case centers on many questions, including why it allegedly took Schettino more than an hour to issue an order to abandon ship.
The trial is running in tandem with the civil suits against Schettino, including the Costa cruise line suit against him for causing the accident and destroying the ship.
The vessel now lies off the coast, half-submerged on its side, CNN said.