More than 700 passengers and crew members aboard a trans-Atlantic cruise have fallen ill with flu-like symptoms, cruise line officials said.

The outbreak, believed to be norovirus, struck people aboard the Carnival Cruise Lines' Liberty, one of the world's largest cruise ships, according to a statement issued Wednesday by the Miami-based company.

The ship left Rome on Nov. 3 with about 2,800 paying passengers and was due to arrive in Fort Lauderdale on Sunday.

"Within 24 hours of sailing, they had a lot of people sick. It has tapered off considerably over the past couple days," said David Forney, with the Centers for Disease Control and Prevention in Atlanta.

He said three environmental health specialists were expected to board the ship in St. Maarten on Thursday to oversee cleaning and to determine the cause of the outbreak.

Noroviruses affect about 23 million Americans annually, according to the CDC. More than a dozen incidents of the illness have been reported on cruise ships this year.