Costa Cruises has offered to pay €11,000 in compensation to each of the more than 3,000 passengers aboard the ship that capsized near the island of Giglio two weeks ago.
The offer, negotiated by Italian consumer groups, is an attempt by Costa Cruises to limit the legal fallout of the accident.
Each passenger would also receive a refund on the cruise and costs of their return home. The offer applies to all passengers, whether a child or an adult, who suffered no physical injuries.
Injured passengers will be dealt with individually.
Those accepting the offer would have to agree to drop all future litigation. They would receive payment within seven days.
Costa Cruises' US parent company Carnival Plc is already facing legal action for compensation.
Codacons, a consumer group which did not participate in the negotiation, is collecting names for a class action suit to be filed in Miami requesting €125,000 for each passenger.
Carlo Rienzi, president of Codacons, said the offer was insufficient and urged passengers to see a doctor to check whether they had suffered psychological trauma.
Roberto Corbella, head of Italy's association of tour operators, and who helped Costa negotiate the offer with the consumer protection groups, urged passengers to accept it.
"Lawsuits have uncertain outcomes, they take a long time, there are legal costs, and some studies indicate that it's not at all certain that passengers would get more than the company is offering," he said.
Crew member Gary Lobaton has already filed a lawsuit against
Carnival in a US district court.
His lawyers said in his court filing that he was not aware of the "dangerous conditions" of the cruise ship until it was too late to abandon it safely.
Yesterday, Italy's top-ranking Coast Guard official, Marco Brusco, said Concordia Captain Francesco Schettino lost "a precious hour", which made evacuating the ship more difficult.
Had the order been given earlier, "the lifeboats could have been launched calmly, people could have been reassured," Brusco said in a Senate testimony.
Passengers have complained the evacuation was chaotic, with some left waiting in lifeboats for two hours before being able to leave the ship.
Several bodies were found by divers in submerged evacuation assembly points, wearing life vests.
So far, 16 bodies have been recovered and 16 are still missing after the 290-metre long cruise liner struck a rock near the Tuscan island.
As divers continued to search the submerged parts of the ship, Dutch salvage team SMIT finalised preparations to remove fuel from the ship's tanks.