The MV Rena struck the Astrolabe Reef some 20 kilometres from the city's Port early on Wednesday morning, sparking a scramble to coordinate a salvage and cleanup operation.
Maritime New Zealand says an observation flight has confirmed the oil appears to have stopped flowing from the ship and the slick is now predominantly sheen, or very thinly spread oil.
Response Manager Rob Service said the oil sheen is moving away from the nearby islands, and spreading westerly about two to five miles from the ship.
"There are darker patches in isolated pockets but they seem to be assisted by yesterday's wind," Mr Service said.
"Obviously from our perspective this is good - we will be continuing to monitor the slick. The observation flights are vital for directing our response, and we are doing these every few hours."
Four vessels from the New Zealand Defence Force have been deployed for the response, comprising Rotoiti, Taupo, Manawanui and Endeavour.
An Iroquois helicopter arrives today and around 500 defence force personnel are on standby for a shoreline cleanup if needed.
Maritime Pollution Response national coordinator Mick Courtnell told a media conference at the Ports of Tauranga he was hoping to get people training in the harbour this afternoon.
Mr Courtnell said there were about 40 people including people who helped with the Gulf of Mexico disaster.
He said they would have the best equipment available.
"By tomorrow we will have the ability to clean up 540 tonnes of oil," he said. "By Monday, we will be able to accommodate more oil than what is out there."
He said there were efforts underway to sort out a way of disposing of the oil. "It doesn't just go down the drain."
Courtnell said about 20 tonnes of oil had escaped the ship - a fraction of the potential 2000 tonnes aboard.
Tomorrow, the team would start getting oil off the surface using two boats with a large floating skirt between them.
Local residents have been quick to rescue oil-coated penguins off the Tauranga coastline near where a container ship has run aground and has leaked oil.
One oiled little blue penguin has been rescued just off Papamoa Beach and one off Little Waihi Beach, while four more were taken for a wash-down after being collected from Motiti Island yesterday.
Papamoa man Brett van Huenen found a penguin about 2.30pm yesterday.
Mr van Huenen and his friend, Adam Coupe, had planned to go fishing in Papamoa East when they came across a large tree branch washed up on the water's edge.
"We were probably about two-thirds of the way toward The Cut when we saw this big tree that was half submerged, then we saw this penguin stuck in the tree.
"It was coated in this thick oil. It was a little blue but it looked pretty black. The oil was really thick."
Mr van Huenen and Mr Coupe managed to free the penguin from the tree before they put it in a container on the front of their quad bike.
"It was struggling and trying to clean itself and get oil off its neck but it looked exhausted."
"It took a little while to get it and I got bitten a few times but we put it in a little box that was covered so it was dark then we took it back to [Karewa Parade] carpark and called the 0800 number."
Two members of the wildlife rescue team collected the penguin and took it back to the makeshift wildlife centre at the Te Maunga wastewater treatment plant.
Another penguin was found at Little Waihi beach about 4pm and taken to the wildlife centre. The two penguins are now recovering under the care of Dr Brett Gartrell, director of New Zealand Wildlife Heath Centre at Massey University.
