Maritime New Zealand says beaches between Papamoa and Maketu in Bay of Plenty will remain closed until all of the oil washed ashore from the Rena is removed.
Earlier this week, the agency said it was possible beaches could reopen this weekend.
Maritime NZ says 737 tonnes of oil has now been pumped off the ship, which went aground on the Astrolabe reef on 5 October.
About 840 tonnes of waste has been removed from the beaches since then.
Maritime NZ says cleanup crews will focus efforts on the beaches between Papamoa and Maketu during the next three days.
Up to 10 tonnes of oil could potentially reach Mayor Island this weekend.
Fresh oiling has been found around Mount Maunganui and Leisure Island, and also along the closed section of beach between Tay Street and Maketu Spit.
It is in a band along the high tide line and up towards the dunes.
Maritime NZ believes the oil lay beneath the sand until it was churned to the surface by tides and rough weather two weeks ago.
A call-out to volunteers was issued on Wednesday. About 200 people are sought to help get rid of oil on the beach at Papamoa.
Help from weather
Calm weather on Thursday is expected help the salvors with the next step in removing oil from the Rena's tanks.
Svitzer Salvage says a new pumping system is being connected to extract oil from the harder to reach parts of the vessel.
The system will take the fuel through a 10cm hose and pump it directly into a tug.
Spokesperson Matthew Watson says it is now a race against the clock to make the most of the calm weather forcast for the next few days.