The crane barge Smit Borneo and the Svitzer-owned tug Singapore are now in port, away from the wreck, and preparing to leave for Singapore.
The last of the operational salvors was demobilised yesterday.
Maritime New Zealand director Keith Manch said the owners and insurers had "for some time" indicated a new contract would be put out for tender when the time came for the removal of the physical wreck.
"That point has now been reached ... [But] it is not clear at this stage how long the tender process will take.
"In the meantime, the owners have indicated that Braemar Howells will remain contracted to the owner to undertake container and debris recovery and monitor the wreck site," he said.
Braemar Howells spokesman Grant Dyson said the company, so far responsible only for container and debris recovery, will be taking on increased duties patrolling the exclusion zone.
"Our role has expanded significantly. We're [now] overseeing the wreck's safety and security.
"We're entering a transition, moving towards wreck removal. Braemar's role in this transitional phase is we've got these additional roles looking after the wreck safety."
But as far as the actual removal of the physical wreck on the reef, he said: "We're not going to be [doing that sort of] a salvage job on what's remaining."
The removal of the wreck must wait until the new salvors are appointed at the conclusion of the tender process, which is expected to close at the end of the month. The current halt to the salvage clean-up would have an impact on local Svitzer sub-contracted crews aboard the Smit Borneo and the tug Singapore.
Mr Manch said the notice for the owners to remove the wreck completely, under the Maritime Act, remained in place and was expected to be fulfilled.
"We share the desire of the local community, and New Zealand as a whole, to have this work completed as soon as possible, and would expect work to resume as soon as practicable after a contractor has been appointed to carry out wreck removal.
"But given the difficulty of the wreck recovery process, and the variability of weather and sea conditions, it is not possible to put a timeframe on completion of the work."