All 197 passengers and crew on the American Heritage cruise ship survived on Friday as well as the crew on the tanker.
Officials said 32 people were brought to the hospital, including two police officers thrown into the Mississippi River when the boat rolled. But none of the injuries were critical and eight remained hospitalised on Saturday.
The National Transportation Safety Board said the tanker's voyage data recorder has been recovered. A 16-member team will spend a week in New Orleans investigating the incident.
NTSB member John DeLeeuw said the agency expected to release a preliminary report within 24 to 30 days, with the final investigation report expected in 18 to 24 months.
The lawsuit, filed by the Board of Commissioners of the Port of New Orleans, said the Atlantic Asphalt tanker caused at least $US1 million ($A1.5 million) in damage to its terminal. A judge issued a warrant on Friday giving federal officials control of the ship for now.
The tanker has been towed away from the site, but it could take weeks to move the cruise ship, which remains turned on its side against a terminal in the Mississippi River, Coast Guard Captain Melanie Burnham told reporters on Saturday.
The tanker appeared to lose steering, but the exact cause of the crash is not known, Burnham said.
The first warning people on board the American Heritage had was the tanker blasting its horn several times as it floated toward the cruise ship, passenger Joe Knab told WDSU-TV.
The hit was hard, and the ship immediately started leaning.
The crew gathered everyone on the third deck to put on life vests and start getting them off the boat, but it suddenly rolled, sending about 100 other passengers and crew into the muddy Mississippi River.
Tugboat operators, other cruise ship captains, nearby workers, police and other rescuers rushed to help.
