WASHINGTON (Reuters) - U.S. Supreme Court justices on Monday for a second time wrestled with an Alaska moose hunter’s claim that the federal government overstepped its authority in banning hovercraft on National Park Service land in the northernmost U.S. state.

FILE PHOTO: A police officer speaks with tourists at the Supreme Court in Washington, U.S., May 14, 2018. REUTERS/Joshua Roberts/File Photo

Hunter John Sturgeon has challenged the U.S. government’s power to prevent him from riding his hovercraft on a river through a federal preserve to reach remote moose-hunting grounds. The case, concerning exemptions given to some Alaska-based waterways from nationwide U.S. regulations, could have bigger implications in other matters, including oil and gas extraction.

During arguments in the case, some of the nine justices questioned the scope of authority that the National Park Service seeks to exercise in Alaska.

Chief Justice John Roberts seemed sympathetic to the hunter, noting the importance of traveling by waterways in the state.

“You may think a hovercraft is unsightly. I mean, if you are trying to get from point A to point B, it’s pretty beautiful,” Roberts, a conservative, told Justice Department lawyer Edwin Kneedler.

In March 2016, when the case first reached the justices, the court ruled unanimously against the government, sending the case back to the San Francisco-based 9th U.S. Circuit Court of Appeals to reconsider a ruling against Sturgeon. The 9th Circuit last year again ruled in favor of the government, prompting Sturgeon to appeal.

There did not appear to be an easy way for the court to decide the case, based on the questions asked by the justices.

“I’ve burned up an awful lot of gray cells trying to put together the pieces of this statute,” conservative Justice Samuel Alito said.

Similarly, liberal Justice Elena Kagan said, “I’m struggling with this.”

People in some parts of the United States, especially western states, have complained about too much federal control of public lands.

Sturgeon was traveling on the Nation River in 2007 in the Yukon-Charley Rivers National Preserve when Park Service rangers detained him, saying he could not use his hovercraft. He argued that the regulation banning hovercraft in federal parks and preserves has no force in Alaska because the river falls under the jurisdiction of the state, which allows hovercraft.

The state of Alaska supported Sturgeon, noting that Congress in 1980 specifically limited Park Service jurisdiction over land within a conservation area that is not federally owned.

The nationwide rule regarding hovercraft, which travel on a cushion of air, dates to 1996.

A ruling is due by the end of June.