Health Minister Katsunobu Kato said the 44 new cases were from another 221 new tests.
They raise the number of infections detected on the Diamond Princess to 218, in addition to a quarantine officer who also tested positive for the coronavirus.
Kato said authorities now want to move elderly people off the ship if they test negative for the virus, offering to put them in government-designated lodging.
"We wish to start the operation from tomorrow or later," Kato told reporters.
Kato added that elderly passengers who have pre-existing conditions or are in windowless rooms would be allowed to leave starting from Friday, rather than the originally targeted date of Feb 19, and complete their quarantine ashore.
About 80 per cent of the ship passengers were aged 60 or over, with 215 in their 80s and 11 in their 90s, according to Japanese media.
"We will make every effort to ensure the safety and peace of mind of the people," Kato told a televised news conference, without confirming the number of passengers who may leave ahead of schedule.
Those who had been in close contact with persons who tested positive would not be allowed to leave the ship, he said.
The Diamond Princess has been moored off Japan since Feb 3, after it emerged that a former passenger who disembarked in Hong Kong last month had tested positive for the virus now named COVID-19.
Of the newly diagnosed infections, 43 are passengers, and one a member of the crew.
The ship was placed into quarantine shortly afterwards and authorities have asked passengers and crew to remain on board until Feb 19.
Those who have tested positive for the new virus have been taken off the ship to medical facilities, but questions have been raised about whether the quarantine on the ship is working, with dozens of new cases diagnosed almost daily.
Passengers are confined to cabins and required to wear masks and keep their distance from each other when they are allowed out for brief periods on open decks.