Diving teams would now spend two working days conducting a visual survey to confirm the changes in the ship's position.
The ship's owner and insurer have also commissioned an underwater sonar survey to create a 3D computer model of the ship's position, and confirm the extent of the movement and any effect this may have had on the structure.
The remaining bow section would also be surveyed.
"The survey will help clarify what impact this movement might have on future salvage operations and any updates necessary to the assessment information of the resource consent application," said Captain John Owen of ship insurers The Swedish Club.
"We're sharing this information now so that the community knows what is happening on site. And to confirm that there will be further delays to our work programme."
A further update would be provided once the survey had been completed and the information "thoroughly assessed".
A baseline survey was last carried out on the ship's position in April 2012, and consistent monitoring of the ship for movement had shown there had been none until now.
Last week, the top half of the ship's accommodation block was removed and transported to the Port of Tauranga.
Meanwhile, a small amount of debris and weathered oil washed up on Mt Maunganui and Papamoa beaches over the weekend during the Cyclone Lusi storm.
Bay of Plenty Regional Council received complaints from beach walkers about oil on the beaches and alerted contractors Envirowaste.
About 20kg of oil and debris was picked up on Mt Maunganui's Main Beach and another 15kg on Papamoa Beach by Envirowaste.
Eddie Grogan, the council's environmental management general manager, said oil and debris on the beach was not unexpected after a storm, given the recent work to remove the top section of the accommodation block.
"It's a timely reminder that there are still small amounts out in the environment, and that's why we have a plan to deal with it after these events.
"We're grateful to members of the public for alerting us to the debris and oil so it can be promptly cleaned up.'
The Rena's owners were adding signs to beach accesses this week providing contact details if anyone finds oil or debris on the beaches.
Numbers to call if people find oil or debris on the beach:
Rena debris Hotline (Envirowaste) 0800 333 771
Regional Council Pollution Hotline 0800 884 883