This morning Maritime New Zealand said assessments of the most vulnerable areas of the coastline would be undertaken today.
So far no oil has been found on any beaches.
Until Monday, when an operation to pump fuel from the 236m cargo vessel gets under way, the only weapon authorities have to fight the worsening spill is spraying dispersant on the murky slick circling the ship.
"It's a very difficult situation and the reality is that we are going to see a significant oil spill," Mr Joyce said.
"So far it's been reasonably small, so I think everybody's preparing for the worst. We are dealing with a very serious situation ... and I don't think anybody is under any illusions."
The vessel is carrying around 1700 cubic metres of heavy fuel oil and it is understood all of the oil leaked so far has come from the pipework of a single 100-tonne tank.
A total of seven birds - five little blue penguins and two shags - have been brought to a wildlife response centre in Te Maunga with oil on their feathers.
The birds are being stabilised and some will be washed today.
It is still not known how the ship struck the reef - nationally renowned for its pristine wildlife - but Transport Accident Investigation Commission spokesman Peter Northcote said three crew members on duty at the time were being spoken to.
Maritime New Zealand's national on scene commander, Rob Service, was unable to say how far the oil could spread in the worst-case scenario of the vessel's entire fuel load escaping.
Resources were pouring in from overseas to assist the 100-strong team Maritime New Zealand has registered in Tauranga. Dozens more volunteers were assisting, including teams combing the beaches on quad bikes.
While spraying a special dispersant had proved ineffective on Thursday, Mr Service said the chemical had worked a little better yesterday.
Temporary caps were meanwhile being placed on the ship's fuel tanks, with the aim of containing all of the oil even if the vessel sank.
"Suffice to say, the vessel is extensively damaged and as time goes by, that damage is slowly increasing," Mr Service said. "The situation is not getting any better ... but the salvors are working hard to rectify the situation and, in particular, to remove that oil."
More resources and special equipment is likely to be needed during the operation. An offshore boom barrier device to ring-fence the oil - measuring about 1250m - was being transported from Australia along with three heavy skimmers to scoop it from the water. A salvage architect was due to arrive from Holland, with further expert help from the Australian Maritime Safety Authority also on their way.
Forest and Bird spokeswoman Karen Baird said many seabird species were particularly vulnerable because they were breeding.
Environmental Defence Society chairman Gary Taylor was worried to see the incident "inexorably moving into a full-scale environmental disaster".
