"It is with a very heavy heart that I need to let you know that we have been unable to locate our guest," he said, according to The Courier Mail.
"We are still in the area of the incident, and the weather conditions with the swell three to four metres high, as you can see outside ... the strong wind made our search extremely challenging.
"As a result we have now made the extremely difficult decision to continue our journey towards Brisbane.
"I know I speak on behalf of all of you when I say our thoughts and prayers are with the family."
A crew member saw the woman fall over the side of the ship about 4pm AEST yesterday afternoon, but the exact details — and the woman's age — have not been confirmed by P&O, the ship's owner.
It's possible the fall was captured on security cameras.
Passengers say her husband saw her fall and went into shock. Life rings were immediately thrown into the water, but there was no sign of her.
One passenger posted on Facebook about the dramatic moment the woman fell.
"She leaned over and the ship rocked in heavy seas — her husband tried to catch her but she slipped," the passenger posted.
Other passengers said children that were near her also witnessed the devastating fall. The woman was believed to be travelling with her children, but it is unclear if they were on the deck with her.
Passengers believe she may have been playing bingo before the tragedy as a woman was heard to say she was going outside because she was unwell. They then heard the alarm being sounded and the woman never returned.
Another passenger, Drew Hulton-Smith, said lookouts had been posted "along all the decks".
The mood on board was "sombre", he said.
"A crew member notified the bridge straight away and the 'man overboard' incident response was activated immediately," said P&O spokesman David Jones.
"In line with this response, Pacific Dawn turned around to follow the course it was on at the time of the incident."
The Australian Maritime Safety Bureau and New Caledonian authorities issued a call for nearby vessels to assist. An AMSA spokeswoman said there are no other rescue boats tasked in the search with the cruise ship alone left to trawl the area.
"It would take days for anyone to reach the area it's so remote," the spokeswoman said.
Passenger Jon Trevithick, posted a picture on Twitter at 5.30pm, of a lone rescue ring in the sea. "Horrendous here on ship," he wrote. "Ship going round and round searching".
"We have been told very little," he tweeted. "I didn't know it was a woman. It happened around 5pm. I was on deck and heard someone cry, 'man overboard'. The ship ground to a halt which took a while, of course. It turned around and found the (possibly second) lifebuoy (pictured).
"Not looking good. Nightfall now. Ship still searching."
Asked if it was "just an exercise" he replied: "This is real."
The search area is understood to be about 1000 kilometres northeast of Brisbane and 300 kilometres west of New Caledonia. The ship was in the Coral Sea, bound for Brisbane on the return leg when the incident occurred.
"We heard the man overboard announcement around 5pm," a Bundaberg woman on board told The Whitsunday Times.
The announcement came over the ship's speakers.
"The boat stopped and turned, life rings were thrown out and we are still searching," the woman said.
"Captain has advised we will continue to search until person is found or until coast guard calls off search."
A Brisbane man holidaying on the ship with his family told AAP conditions in the search area are rough, with 3 to 4 metre swells.
He said little information was being given to passengers about the situation other than they were searching for the missing woman. The ship had been on a week-long cruise of Pacific Islands, leaving Brisbane last Saturday.
The 245-metre long Pacific Dawn has a capacity of more than 1500 guests across 11 guest decks, according to the P&O website.
The 27-year-old ship underwent major refurbishment last year, with new restaurants and cafes, an update interior, and a waterpark added.
- With AAP
