The removal of heavy fuel oil from the Rena is almost finished.
Maritime New Zealand says salvors will next start preparing to offload containers from the ship.
Nearly two-thirds of the 358 tonnes of oil in the ship's submerged starboard number five tank has been pumped into the Awanuia, a tanker barge.
Although stripping remnants of accessible oil would go on for some time, Maritime NZ says the job of removing the bulk of it is about complete.
Pumping of fuel oil from the ship stopped at about 1am on Sunday and will resume when the remaining oil has risen to the top of the sea water in the tank.
The Go Canopus, which came into port on Saturday to discharge oil from the engine room, has returned to the Rena.
Sea Tow 60, a giant barge, is being prepared to be moored alongside the Rena, so that containers can be removed, a process that is expected to take a couple of days.
The Rena was carrying 1368 containers when it ran aground on the Astrolabe reef off the coast of Tauranga on 5 October. Eighty-eight have since been lost overboard.