The 30-year-old man and 27-year-old woman were discovered missing after the Carnival Spirit docked at Sydney's Circular Quay today morning, said New South Wales state Police Superintendent Mark Hutchings.
"We believe they have gone overboard," he told reporters, adding that there was "a chance that they may be" alive.
"This is a tragic event at the moment, but we're holding out hope we might be able to find these people alive," Hutchings said.
The passengers were discovered unaccounted for during the debarkation process, said Peter Taylor, spokesman for the ship's operator, Carnival Cruise Lines.
"The guests in question were travelling with family and friends, and initial reports indicate that the couple was last seen onboard the vessel last night," Taylor said in a statement.
"The ship immediately initiated standard missing person procedures, including a full search of the vessel, as per protocol," he said.
Carnival Cruise Lines is a subsidiary of Miami-based Carnival Corp, the world's largest cruise operator.
Carnival Corp. Has been plagued by a series of high-profile problems in recent years. Last year, the Costa Concordia ran aground off the coast of Italy, killing 32 people.
Also last year, the Costa Allegra caught fire and lost power in the Indian Ocean, leaving passengers without working toilets, running water or air conditioning for three days.
In February, passengers aboard the Carnival Triumph spent five days without power in the Gulf of Mexico after an engine-room fire disabled the vessel. Those on board complained of squalid conditions, including overflowing toilets and food shortages.
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