Demonstrations against a giant telescope planned for Hawaii's tallest peak have spread to New York, Las Vegas and Honolulu's tourist mecca of Waikiki as Native Hawaiians push to protect what they say is a sacred place.

In Nevada, a few hundred Native Hawaiians and former Hawaii residents gathered under the famous "Welcome to Fabulous Las Vegas" sign to show their solidarity with protesters back home.

Elsewhere, video on Twitter showed a few dozen protesters chanting and holding signs and flags in New York's Union Square.

Protesters have been blocking a road to the summit of Mauna Kea, a site they consider to be sacred, since last week to prevent construction of the Thirty Meter Telescope.

State officials said the crowd stood at 1,500 on Monday after swelling to 2,000 over the weekend.

Hawaii Lt. Gov. Josh Green said there will have to be a compromise in order for the telescope project to go forward but he doesn't know if that's possible.

Even though the Hawaii Supreme Court has ruled the telescope's construction permit was valid, the question at hand is not a legal one, he said.

"This is a cultural question and the question about an entire culture's sense of self. I don't care what the rulings were. It boils down to how the Hawaiian community perceives itself and what vision it has for the future," Green said in a telephone interview after visiting the protest site. He said he spoke with Native Hawaiian elders for four hours.

The lieutenant governor said it's time for a "grand reconciliation" with Hawaii's "host culture."

He said that means the state taking a strong position on U.S. recognition for Native Hawaiians, moving more aggressively to provide house lots through the state Department of Hawaiian Homelands and not "shying away from" the U.S.-backed overthrow of the Hawaiian Kingdom in 1893.

He said he would urge Gov. David Ige to de-escalate the situation and withdraw the Hawaii National Guard. Ige has sent guard units to the mountain to transport personnel and supplies and enforce some road closures.

Protests also spread to the tourism sector, the state's biggest employer.

Several businesses joined a one-day "tourism boycott" organized by activists.

Old Lahaina Luau on Maui called off its nightly luau, leading to cancellations for 450 people. Because the show is sold out through the middle of next month, it wasn't able to accommodate most guests on another night and issued refunds.

The company acted because it believed most of its employees would likely have decided to join the boycott regardless.

"So we decided, you know what, it would really show our support to our employees and at the same time reflect our support to Hawaiian culture for us to have everyone be able to take off that day," said Kawika Freitas, director of public and cultural relations at Old Lahaina Luau.

Skyline Hawaii suspended zipline rides on the Big Island, Kauai and Maui. It cancelled bicycle and van tours to the summit of Haleakala, Maui's tallest peak, and to the small town of Hana. The decision affected several hundred customers.

"We did have a few people that were a little bit upset, but 90 percent of the people were very understanding," said Jennifer Puha, who works in reservations.

The company's owner has a lot of respect for Hawaiian culture, Puha said. "He feels that we have a duty to stand by doing the right thing," she said.

Both Skyline Hawaii and Old Lahaina Luau were to resume normal operations on Tuesday.

Over the weekend, hundreds of people marched on sidewalks past tourists and high-rise hotels in Waikiki.

Scientists want to build the telescope atop Mauna Kea because it is one of the best sites in the world for viewing the skies. The observatory would join 13 other telescopes already at the summit, though several are due to be decommissioned in a concession to telescope opponents.

Ige has ordered the closure of the road as a way to clear a path for construction equipment. But protesters have blocked the road, creating a standoff.

On Monday, 13 state lawmakers and county council members called on Ige to rescind his emergency proclamation for the area, saying it violated the spirit of a law intended to help communities during natural disasters or threats to public safety.

They said neither describes the current situation.