The combatants in the Thirty Meter Telescope dispute are not only skirmishing at a state hearing in Hilo, but crossing swords at the state Supreme Court.

University of Hawaii-Hilo attorneys filed a motion with the high court Monday to dismiss an appeal by the Mauna Kea Hui petitioners challenging a number of due-process decisions made in the contested-case hearing.

State attorneys filed a similar motion Thursday, saying the appeal is premature and invalid under state law.

In addition, the university is strongly suggesting that the Supreme Court appoint a master to help oversee the contested-case hearing in a move to ensure compliance with the court’s decision ordering the do-over of proceedings.

The state Supreme Court in December instructed the state Board of Land and Natural Resources to hold a new contested-case hearing because of a due-process error in approving the project before holding the 2011 hearing. By formally approving the project first, the board failed to consider the evidence presented during the hearing, the court said.

The new hearing, now in its evidentiary phase, continues at 9 a.m. today at the Grand Naniloa Hotel in Hilo and is expected to last into next month.

The appeal by the Mauna Kea Hui petitioners was filed with the high court Nov. 7. It questions a variety of due-process decisions made at the contested-case proceeding by hearings officer Riki May Amano and the Land Board, from affirming the hearings officer and validating the permit application to limiting each party’s questioning of a witness to 30 minutes.

Honolulu attorney Richard Naiwiehu Wurdeman said Monday that the board has consistently failed to follow the Supreme Court’s mandate to follow due process and conduct a fair and impartial process.

Wurdeman filed the appeal directly to the Supreme Court because of a law that took effect in August that allows certain contested-case hearing decisions to bypass the Intermediate Court of Appeals.

Approved by the 2016 Legislature, the law was intended to streamline the appeals process and prevent major projects, such as the planned $1.4 billion TMT, from languishing in the courts for years.

“These issues will ultimately be dealt with on appeal, nonetheless, one way or another,” Wurdeman said in an email. “The University of Hawaii should actually welcome the Supreme Court’s review at this time, rather than oppose it, and seek the truth and what is just.”

According to the university’s motion to dismiss, the new law doesn’t allow for an appeal just yet because the hearing has not concluded and the issues are not final.

“We filed this motion to dismiss because we believe there is no merit to this appeal,” university spokesman Dan Meisenzahl added. “We look forward to completing a fair and impartial process.”

In its motion, the university suggests that a master be appointed over the case in light of its complexity, the number of parties and growing voluminous record.

The contested case involves 25 separate parties and is expected to take at least 21 hearing dates over several months to conclude. To date, the docket shows more than 410 entries with substantial issue-­oriented filings from the various parties.

“Thus, any subsequent judicial review will require consideration of a vast volume of material,” the motion said. “Due to the complexity of this proceeding and the public importance of the issues raised herein, a master could substantially aid the parties, the hearing officer, the board and/or this court (in the event of a future appeal).”

It’s uncertain, however, how much power a court master would have over such a contested-case hearing. The specific duties are not spelled out in the law.

Wurdeman is the same attorney who earlier cited scheduling conflicts in withdrawing from representing the Mauna Kea Hui at the hearing. The group includes Kealoha Pisciotta of Mauna Kea Anaina Hou, Clarence Ching, the Flores-Case Ohana, Deborah J. Ward, Paul Neves and ­KAHEA: The Hawaiian Environmental Alliance.

The Thirty Meter Telescope, billed as one of the largest and most powerful telescopes in the world, was scheduled to start construction last year and become operational in 2024. But protesters blocked construction crews from reaching the mountaintop work site on several occasions in 2015 before the high court invalidated the work permits and ordered a new contested case in December.