The two complaints, lodged on behalf of several Bay of Plenty groups and individuals, centre on an order by the Government for the ship's owners to remove the vessel from Astrolabe Reef off the Tauranga coast, where it ran aground in October 2011.
Maritime New Zealand issued the order hours after the grounding, and an agency spokesman yesterday confirmed that it remains in force.
In light of that, the iwi groups are questioning why the ship's owners have proposed leaving much of the wreck on the reef.
"The order hasn't been actioned, and it appears to iwi what is happening is that rather than enforcing the removal notice, there is something happening which would allow the insurers to leave the wreck there," said environmental consultant Buddy Mikaere, who is working with some of the complainants.
"So the iwi position is that there's an obligation on the Crown to follow up on its removal notice. The question being asked is, why haven't you asked them to take it away?"
The tribunal has asked the Crown and interested parties to respond to the claims by the end of the week.
A Maritime New Zealand spokesperson said that in order to lift the order an application would have to be made under the Resource Management Act (RMA).
The agency's director would have to be satisfied the wreck had been safely dealt with by other lawful means - most likely to be the RMA.
Mr Mikaere believed the issue was a Treaty matter as leaving the wreck on the reef affected Maori cultural and spiritual values.
"There's a fair degree of frustration about the whole process."
He has also been involved in appeals against a Bay of Plenty Regional Council decision proposing to temporarily remove the reef's status as an "outstanding natural character feature".
While different iwi had stated varying positions at times, the most recent consensus favoured having the wreck taken away and restoring the reef back to its former state, said Awanui Black, chairman of the Te Moana a Toi Iwi Leaders' Forum.
Despite their concerns, he said relations with the ship owners had been positive.
Across the wider Bay of Plenty community, the fate of the Rena has divided opinion, with some happy for it to stay on the reef and others - among them Tauranga Mayor Stuart Crosby - wanting it gone.
Green MP Gareth Hughes said the decision was for Bay of Plenty residents to make, but believed the owners should only be working toward the removal order while it is still in place.
The owners and insurers have explored options for the ship's future and have proposed leaving part of the wreck in place after cleaning up the site and making it safe.
Meanwhile, a large stage-by-stage clean-up and salvage operation is continuing, and an assessment of the environmental, cultural and social impacts, including further sediment sampling on the reef, are to be completed.
A spokesman said this would be made public before the end of the year.
"Until then, any decision to apply for resource consent to leave parts of the remaining wreck in a safe and responsible state won't be made.
"Having spent $300 million on operations so far and counting, the owner and insurer's approach right from day one has been to work with authorities and the community to seek the most safe and responsible outcome for the Bay of Plenty community, its environment and the salvage teams involved."
• Salvors have yet to finish reducing the Rena's bow to 1m below sea level. More than 650 tonnes of debris have been removed from the sea floor; this work will continue throughout the year. Debris from cargo hold four is being cleared to recover two remaining containers of plastic beads. Dive surveys of cargo holds five and six will then be done to identify the state of the four remaining containers of interest in the sunken stern.
• The ship's insurers are to firm up an $11.5 million limitation fund for compensation claims. The cap was challenged in the High Court, but a decision in April backed the fund. A separate $1 million compensation fund offered as a goodwill gesture by charterer Mediterranean Shipping Company opened this month.
• Two major reports are due. An internal review by Maritime New Zealand into how it responded to the grounding is expected shortly, while a large report into the disaster by the Transport Accident Investigation Committee is not due before September. The Waitangi Tribunal is urgently considering fresh claims by iwi groups pushing to rid Bay of Plenty waters of the wrecked cargo ship Rena.