His publicist, Melissa Booth, said Jackson was "doing well" but would remain at Wellington Hospital for at least a few more days. Booth said doctors expect the director to make a full recovery.
Jackson was admitted to Wellington Hospital last week for severe stomach pains.
His health has delayed the start of filming of "The Hobbit," the two-part prequel to the "Lord of the Rings" trilogy.
Production of "The Hobbit" had previously been troubled by financial issues and the departure of its initial director Guillermo del Toro.
The Associated Press contributed to this report.