This week a coalition of activists led by Kealoha Pisciotta filed a legal challenge in the Third Circuit Court of Hawaii, seeking an injunction against the telescope construction. The TMT International Observatory, the activists said, had failed to post a security bond that is required under a 1977 plan that governs the management of the mountain. The bond, in the amount of the full cost of the project, would cover the cost of restoring the site to its natural state once the telescope has finished its mission.

“By failing to post the bond, they have laid all financial liability on the People of Hawai’i, in the event the TMT doesn’t get full funding,” Ms. Pisciotta said in an email. “And this is especially important because they don’t have full funding now.”

In an email, Douglas Ing, a lawyer for the observatory, said: “We had a brief opportunity to review an unfiled copy of a lawsuit. We believe this is a weak lawsuit and we expect to defeat it.”

It is only the latest chapter in a long series of protests and legal skirmishes. In December 2015, the state’s Supreme Court invalidated a previous construction permit on the grounds that the project’s opponents had been deprived of due process. A state board had granted the permit before the opponents could be heard in a so-called contested case hearing.

The TMT astronomers said they would build their telescope in the Canary Islands if denied in Hawaii. Last October, the Hawaiian Supreme Court restored the telescope’s building permit. Earlier this summer, Governor Ige announced that a “notice to proceed” had been issued, allowing construction. As part of the deal, five telescopes currently operating on Mauna Kea will be shut down and their sites restored to original condition.

Mr. Ige said the environmental reviews required for the decommissioning of two of those telescopes had already begun.