ROME — Costa Crociere SpA is offering uninjured passengers $14,460 apiece to compensate them for lost baggage and psychological trauma after its cruise ship ran aground and capsized off Tuscany when the captain deviated from his route.

Costa, a unit of the world’s biggest cruise operator, the Miami-based Carnival Corp., also said it would reimburse passengers the full costs of their cruise, their travel expenses and any medical expenses sustained after the grounding.

The agreement was announced today after negotiations between Costa representatives and Italian consumer groups who say they represent 3,206 cruise ship passengers from 61 countries who suffered no physical harm when the Costa Concordia hit a reef Jan. 13. So the deal would total more than $46,000,000.

The deal does not apply to the hundreds of crew, the roughly 100 cases of people injured or the families who lost loved ones.

Passengers are free to pursue legal action on their own if they aren’t satisfied with the deal. Some consumer groups have already signed on as injured parties in the criminal case against the Concordia’s captain, Francesco Schettino, who is accused of manslaughter, causing a shipwreck and abandoning the ship before all passengers were evacuated. He is under house arrest.

In addition, Codacons, one of Italy’s best known consumer groups, has engaged two U.S. law firms to launch a class-action lawsuit against Costa and Carnival in Miami, claiming that it expects to get anywhere from $164,000 to $1.3 million per passenger.

Codacons has also called for a criminal investigation into the not-infrequent practice of steering huge cruise ships close to shore to give passengers and residents on land a thrill.

The chief executive of Costa, Pier Luigi Foschi, told an Italian parliamentary committee this week that so-called “tourist navigation” wasn’t illegal, and was a “cruise product” sought out by passengers and offered by cruise lines to try to stay competitive.

The Concordia gashed its hull on reefs off the island of Giglio after Schettino made an unauthorized deviation from its approved route. Some 4,200 passengers and crew were hastily evacuated after the Concordia ran aground and capsized a few kilometers away near the port of Giglio.

Sixteen bodies have been recovered and another 16 remain unaccounted for and presumed dead.