Removing the containers from the grounded Rena is likely to take a "significantly long period of time", perhaps stretching well into next year, officials say.
But the removal of the 1288 containers left onboard could not begin until all of the oil had been pumped from the ship.
Transport Minister Steven Joyce also told media this afternoon that the cost of the clean-up - which does not include the salvage of the ship - had risen to $10 million.
Salvors have now emptied the stricken vessel's port-side 5 tank, bringing the total amount of oil pumped off to 808 tonnes and leaving 575 tonnes onboard.
Their next step is to clear the settling tanks within the engine room, holding about 228 tonnes of oil.
Maritime New Zealand advisor captain John Walker said work was continuing to build a dry "coffer dam" through a corridor in the ship to the submerged starboard-side tank, holding a further 358 tonnes.
A dive team were working beneath oily water and in pitch-black conditions to clear the way.
Prime Minister John Key visited a salvage team in Mt Maunganui this morning and later paid tribute to their work.
"They are as confident as they can be, notwithstanding the very challenging situation that they face," he said.
"This is one of those stages where it's a little stop start and they're at stop at the moment. I think we should congratulate them - they're working in a very difficult environment. They're very dangerous conditions, they're moving heavy equipment round and they're in pretty new territory with some of the things they are doing."
Clean-up teams were on the beaches along Mt Maunganui today after small deposits of oil washed up.
National on-scene commander Nick Quinn said the clean-up would soon move into a second phase where mechanical equipment was used to sift remaining oil from the sand.
Penguin enclosure race is on
The race is on to complete specialised penguin enclosures which will give hundreds of birds affected by oil from container ship Rena a new lease on life.
By lunchtime today builders were due to have completed six specialised penguin enclosures, each measuring 6m by 9m.
About a dozen builders aim to finish four more enclosures by the end of next week for long-term care of the 314 penguins at the Wildlife Rescue Centre at Te Maunga.
Each enclosure can house up to 30 penguins and includes a large pool where they can swim and play, as well as large communal areas where they can preen and feed.
Wildlife Recovery Centre facility manager Bill Dwyer and his team began building the first penguin enclosure on Sunday and had begun five more since Tuesday.
He is in charge of deciding where buildings and tents will be erected at the Wildlife Recovery Centre - a role he's had since Rena struck the Astrolabe Reef and started leaking oil into the ocean three weeks ago.
Mr Dwyer said he was not sure how long the birds would remain inside the enclosures but they could be a long-term solution if necessary.
"As long as there's an issue with oil, these penguins can stay as long as they like," he said.
Until now, the penguins have been living in small basket-like enclosures, being taken to a pool to swim.
Working on the task had been challenging as he had never made a penguin enclosure before, Mr Dwyer said. However, it was a rewarding experience.
He is a member of the New Zealand Wildlife Health Centre at Massey University in Palmerston North and worked in the wildlife recovery after the Jody F Millennium spill in 2002. However, there were more birds to deal with this time.
"We didn't know how to approach this so [we] drew up a plan and sort of went from there," he said.
The 314 penguins in the Wildlife Recovery Centre get fed twice a day and eat five to seven fish at each feeding.
They also have one swim a day, which lets them condition and preen their feathers - crucial for re-waterproofing.
Oiled Wildlife Response manager Kerri Morgan said it was important to monitor the penguins' health and condition, especially at feeding times.
"Correct feeding is a critical part of the rehabilitation process and our staff take great care when feeding the penguins," Ms Morgan said.
"We use either sprats or anchovies and need to ensure that none of the natural oils from the fish get on the birds' feathers, as this can damage their natural waterproofing."
It was too early to tell when the penguins could be released but the focus was on ensuring they were all healthy and well-nourished before being released back into the wild, she said.
All the penguins were "doing really well and have a great fighting spirit".
The centre has 379 birds in its care.
A further 1370 birds have died, and investigations are being carried out to determine whether oil was the cause of death.
Shock for Rena salvors
Divers assessing the partially-submerged fuel tank on board the Rena got the shock of their lives when they found a power system inside the stricken ship still operating.
Maritime New Zealand salvage unit manager Bruce Anderson said divers were assessing the starboard number five tank yesterday when they found power still operating inside the damaged hull - three weeks after the container ship hit the Astrolabe Reef.
"They suddenly found the switch and turned it off,'' he said.
"Fortunately no one was injured in that.''
Volunteers will be cleaning up fresh oil found around Mount Maunganui and Leisure Island and between Tay Street and Maketu Spit today.
"This looks like oil that was buried under the sand during the rough weather that occurred a couple of weeks ago,'' National On Scene Commander Nick Quinn said.
"The movement of tides and sand has brought it again to the surface, and so we now have a new layer of oil to remove.''
Mr Quinn said the oil had settled in a band along the high tide line and up towards the dunes.
During the past three days, about 848 tonnes of waste was collected off beaches.
The coastline from Papamoa to Maketu would remain closed, and experts are conducting regular water sampling.
Meanwhile, pumping had temporarily stopped from the port number five tank yesterday as salvors moved the pump deeper into the tank.
"Most of the oil has been removed from that tank, so the fuel transfer rate out of there is slowing down,'' Mr Anderson said.
The salvage team had begun pumping fuel from the engine room tanks into the port number five tank but this had proved ineffective, Mr Anderson said.
Salvors were now working on a pumping system to take the fuel through a 10cm hose and directly into the anchor-handling tug Go Canopus.
The bollard tug replaced the Awanuia and established a connection with Rena last night.
About 737 tonnes of oil had been taken off the vessel in total.
Mr Anderson said the Go Canopus was capable of maintaining a close position to the ship in poor weather conditions, however, the weather forecast for the next five days was relatively clear and pumping was due to continue throughout this time.
Pumping to the Go Canopus was likely to be slower than using ship pumping equipment and existing pumping methods but was the best option available, Mr Anderson said.
Salvors continued to focus on removing oil from the starboard number five tank and would then shift their attention interests to the three settling tanks, which hold 112, 116 and 25 tonnes respectively.
"This is really challenging as the tank is under water and the team needs to create a water-tight space to work from,'' Mr Anderson said.
As far as container recovery went, Mr Anderson said it was highly likely containers would be recovered in pieces rather than intact.
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