Late last year the 91,740 GT ship experienced problems with its Azipod system in Singapore at the start of the first NCL Asia program in over a decade.
Now Norwegian Star has further technical malfunction and is sailing at reduced speed.
She will visit Dunedin on February 13, Akaroa on February 14 and Wellington on February 15, but will miss Napier on February 16.
The ship will arrive in Tauranga on February 17, and Auckland as planned on February 18.
All passengers are being offered a credit of A$1,000 per stateroom and a 100% future cruise credit of the fare paid for use within the next five years.
Passengers who sail on the February 6 voyage will receive a A$250 shipboard credit and a 25% credit on the fare of a future cruise to be used within five years.
Those who do not sail on the voyage to Auckland will receive a 100% future cruise credit.