New Zealand spokesman Vince Cholewa said today no new information had come to hand since the search was "postponed" about midday on Monday.
While search areas were calculated according to information about what the man was wearing, currents and tides, there was no information available as to whether currents might carry the man towards the Hawke's Bay coast.
But he said anyone who came across anything which might be relevant should contact authorities immediately.
Police reported late on Tuesday only that inquiries were continuing.
It is thought to have been the first fall from the Norwegian Jewel since it was launched in mid-2005. It has capacity for almost 2400 passengers was in the third of six visits to Napier during the 2019-2020 summer, the next three all in the next five weeks.
But man overboard websites report at least seven incidents involving the 16-strong NCL fleet in the last two years, but they include several rescues.
Just seven weeks ago a woman fell from the Norwegian Sun near Freeport in the Bahamas. Crew were praised for the rapid deployment of the rescue craft and rescue of the woman within 20 minutes.
A 63-year-old Korean woman disappeared after falling from the Norwegian Epic in the Mediterranean Sea in June, but in 2018 two female passengers and a Filipino crewman were rescued, one woman surviving about 10 hours in the sea after a fall from the Norwegian Star about 60 miles off the coast of Croatia.