Maritime New Zealand said the current sea state, combined with the dangerous state of the wreck, is preventing dive operations at this stage but the swells are expected to ease over the next few days.
The Svitzer salvage dive team will remain on standby.
More than 150 responders helped in the Braemar Howells-led container and debris recovery operation today.
Twelve vessels, including specialist tugs, barges and rapid response vessels were on the water corralling and collecting containers and debris.
The operations focused on areas north west of the Astrolabe Reef and north of Motiti Island, as well as near Waihi Beach.
Six containers were removed from Waihi Beach. Another 10 are still to be removed from the area between Bowentown and just north of Waihi Beach, and 11 containers will be removed from Matakana Island as soon as possible.
Oiled wildlife response teams scouring beaches for affected wildlife found one oiled penguin. The penguin was taken to the oiled wildlife facility at Te Maunga.
Currently, there are six little blue penguins in care at the Te Maunga facility. There are 22 little blue penguins, two fluttering shearwaters and one dotterel in care at Massey University in Palmerston North, where they were taken when the Te Maunga facility was wound down.
The birds will be released back into the Bay of Plenty when their habitats are ready for their return.
Maritime New Zealand said there was no further oil leaking from the wreck.
On-scene Commander Alex van Wijngaarden said there were 12 patches of oil about 100 by 50 metres wide but they appeared to breaking down gradually.
He said they were likely to come ashore.
"The amounts of oil we're dealing with are small, we do remain ready to respond and escalate if this is needed and our trajectory modelling now shows that possible impact from Little Waihi to Pukehina probably late Thursday evening.''
There has also been an assurance that it was business as usual in Tauranga and Mount Maunganui despite debris from the Rena washing up.
Associate Minister of Transport Chris Tremain said both areas are open for business.
"The beaches are not closed and while there is some inconvenience in access caused by the machinery that's picking up the timber packs, we want to make it clear that Tauranga is very much open for business.''
Meanwhile the owner of the Rena is silent on whether it will pick up the whole cost of the clean up.
In a statement today, Costamare Shipping said its insurers are continuing to fund the salvage operation, including the recovery and processing of containers washed overboard.
But the company has not responded to queries about whether it will pay for the beach clean up and foot the entire bill of the cost of the disaster as demanded by Transport Minister Gerry Brownlee.
Maritime Lawyer Peter Dawson said he was not surprised.
"Owners' obligations as far as the clean up is complicated, it would be very difficult for the owner to make an unequivocal statement to what the obligations are and I would be surprised if they did so.''
Mr Dawson said the law states only that the vessel must be removed if it constitutes a hazard to navigation.
"If it isn't a hazard to navigation and it sinks so deep that it doesn't present a hazard to navigation then there would be a question mark in my mind over the obligation to remove it.''
