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.
