Story highlights NEW : Search called off late Friday afternoon

: Search called off late Friday afternoon The couple was at the end of a 10-day Pacific Island cruise.

Police believe the two went overboard Wednesday night

They were reported missing when the Carnival Spirit docked in Sydney

After scouring hundreds of miles of waters off Australia's coast, authorities on Friday called off a search for two cruise ship passengers who are believed to have fallen overboard.

The 30-year-old man and 27-year-old woman were reported missing when the Carnival Cruise ship Spirit docked in Sydney on Thursday morning, CNN affiliate Seven Network reported. The first clue came when they didn't claim their luggage.

Maritime officers reviewed surveillance video from the ship and determined that Paul Rossington and Kristen Schroder went overboard Wednesday night. Authorities believe the couple fell about 150 kilometers (93 miles) off Foster, New South Wales.

"We believe that they were up mid-deck, which is halfway up the side of the ship, which is quite a way to fall," said Detective Superintendent Mark Hutchings of the New South Wales Police Marine Area Command.

Late Friday afternoon, New South Wales police said they called off the search after finding no sign of the couple. The search, involving an Australian navy ship, the police force's marine unit and the Australian Maritime Safety Authority, covered 1,360 square nautical miles, they said.

The couple was sharing a cabin and traveling with family and friends on a 10-day Pacific Island cruise. Police said they are investigating the fall.

Schroder's family issued a statement thanking "everyone involved in the search for both Paul and Kristen."

"We would appreciate privacy and understanding while we come to terms with our beautiful girl's tragic accident," the family said.

Carnival has been plagued by a series of high-profile incidents recently.

In February, an engine room fire left the Carnival Triumph adrift in the Gulf of Mexico, with passengers reporting overflowing toilets and human waste running down the walls in some parts of the ship.

On a March cruise, the Carnival Dream lost power, and some toilets stopped working.