The ship has already spilled hundreds of tons of oil, and workers are in a race against nature to try to drain the fuel before waves break up the vessel, which has begun to crack apart.
Last week, crews removed about 10 tons of oil before the weather forced them to postpone the work.
On Friday, the calmest weather in days allowed the crews to get back aboard the ship, but the complexity of their task dashed earlier hopes they might resume pumping that day, according to Maritime New Zealand, which is managing the operation.
Crews began attaching four platforms to the port side of the vessel to form a flat surface for pumping out the port tanks, Maritime New Zealand said in a release. The agency didn't offer a new timeline for when pumping might begin.
Environmentalists have warned of a disaster for wildlife if all the ship's 1,870 tons (1,700 metric tons) of oil and 220 tons (200 metric tons) of diesel is allowed to spill into the ocean.
Meanwhile, several of the 88 containers that have fallen off its deck had washed ashore by Friday, and authorities confirmed one container that toppled overboard contained a hazardous substance. However, an official said it should not pose a major threat.
Heavy seas had kept salvage crews away from the 775-foot (236-meter) Liberian-flagged Rena for days, but better weather Thursday allowed crews to board the vessel for about six hours to check systems. The Rena ran aground Oct. 5 on Astrolabe Reef, 14 miles (22 kilometers) from Tauranga Harbour on New Zealand's North Island.
Ewart Barnsley, another spokesman for Maritime New Zealand, said the salvage crew found oil hoses and pumps for transferring fuel largely undamaged aboard the ship. They also concluded that the ship was safe to work from. Barnsley said a barge was moored nearby to receive oil.
Marine New Zealand salvage manager Bruce Anderson said the vessel has appeared to have stopped moving, which was necessary before pumping operations can resume.
A vertical crack in the ship runs around the entire vessel -- meaning the ship is now only held together by its internal components, said Steve Jones, another spokesman for Maritime New Zealand.
"The reality is the vessel could break up at any point," Jones said.
The ship's 44-year-old Filipino captain was charged Wednesday with operating a vessel in a manner causing unnecessary danger or risk and was released on bail Wednesday at Tauranga District Court.
The ship's second officer appeared in the same court Thursday on the same charge. Judge Robert Wolff made orders suppressing publication of the defendants' names for the sake of their personal safety.
If convicted, each could face a fine of up to 10,000 New Zealand dollars ($7,800) and 12 months in prison. Their next court appearance is Oct. 19, when authorities say more charges are likely.
The government has demanded to know why the ship crashed into the well-charted reef in calm weather, but the vessel's owner, Greece-based Costamare Inc., has given no explanation.
Costamare released a statement this week apologizing for the incident and said it was investigating how the ship could have run aground.
"Our Captain is an experienced Master and has an exemplary record," Costamare managing director Diamantis Manos said in the statement. "The ship was fully certified and had recently been inspected ... They found no problems. Obviously something went very wrong and we will cooperate with the Transport Accident Investigation Commission of New Zealand (TAIC) to find the answer."
Maritime New Zealand estimates that at least 390 tons (350 metric tons) of heavy fuel oil have spilled from the hull, leading New Zealand's environment minister, Nick Smith, to call it the country's biggest maritime environmental disaster.