Maritime New Zealand says the leak appears to be intermittent and coming from damaged pipes rather than from fuel tanks, but it remains hard to assess given the extensive damage to the vessel.
The 775-foot (236-meter) Liberia-flagged Rena struck the Astrolabe Reef about 12 nautical miles from Tauranga Harbor early Wednesday and has been floundering there since.
The agency says the 25 crew on board are safe and trying to stop more oil from leaking.
The agency said Thursday that four seabirds have died in the oil slick, which extends about three miles (five kilometers) from the ship. The agency plans to apply the dispersant Corexit 9500 on Friday.