Costa Cruises, the Italian company that owns the capsized cruise ship Costa Concordia, has offered passengers 11,000 euros ($14,000) each in compensation.
The deal comes after negotiations between Costa Cruises and several Italian consumer groups.
Costa Cruises also promised to refund medical and transport expenses, as well as the cost of the cruise.
One consumer group, Codacons, has urged passengers not to accept the offer, Reuters news agency reports.
Codacons and two US law firms are filing a class-action lawsuit in the US suit against Costa Cruises, demanding at least $160,000 for each passenger on the ship. Costa Cruises is owned by the US-based Carnival Group.
Mitchell Proner, a lawyer with one of the firms filing the lawsuit, said last week that it was being brought on behalf of 110 claimants.
A crew member from the Costa Concordia has also brought a lawsuit against Costa Cruises in the US state of Illinois, Reuters reports.
In court documents, Gary Lobaton says he was not aware of the “dangerous conditions” the ship was in until it was too late to abandon ship.
The deal will not cover those passengers who lost loved ones or who were injured.
“This deal concerns some 3,000 passengers from 60 countries, including some 900 Italians,” Adoc, one of the consumer groups that negotiated the agreement, said in a statement, AFP reports.
“We think around 85% of them will agree to this deal,” it added.
On Tuesday another body was found inside the wreck of the Costa Concordia, bringing the death toll to 16. At least 16 others are missing.
Costa Concordia cruise ship ran aground off the Tuscan island of Giglio on 13 January with more than 4,200 people on board.
Costa Cruises has blamed Captain Francesco Schettino for committing “grave errors of judgement” by steering the ship too close to Giglio on an “unauthorized manoeuvre”.
Francesco Schettino is currently under house arrest on suspicion of manslaughter, which he denies.