An American man is believed to have fallen overboard from a cruise ship which arrived in Sydney this week.

A steward aboard the Golden Princess liner raised concerns about the 61-year-old's whereabouts on Wednesday after he joined the South Pacific cruise in Noumea.

NSW Police and the Australian Maritime Safety Authority were alerted after a thorough search failed to find the missing passenger, a Princess Cruises spokesman told AAP on Friday.

"Having ruled out other possibilities, this is being treated as a man overboard incident," he said in a statement.

"Our thoughts and prayers are with the guest's family in America with whom we have communicated directly since he was reported missing."

The 61-year-old was travelling alone.

The Golden Princess arrived in Sydney on Thursday after completing a 13-day round-trip cruise to Fiji and other South Pacific destinations.

It was cleared to depart the city again on Thursday night bound for Papua New Guinea.

The ship's CCTV footage has been reviewed.

AAP

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