AQUINNAH, Mass. — The state of Massachusetts and an Indian tribe whose ancestors first inhabited Martha’s Vineyard are asking a federal judge to settle whether the tribe can build a casino on the island that has long been a favored vacation destination for the rich and powerful. The Aquinnah Wampanoags want to turn an unfinished community center on the remote, western side of the island into a gambling hall filled with electronic betting machines.

They say the federal Indian Gaming Regulatory Act permits them to offer certain types of gambling because they are a federally-recognized tribe with jurisdiction over about 485 acres in the town of Aquinnah. They say recent legal analysis from other federal authorities support that claim.

“This court cannot properly conclude that the Commonwealth has jurisdiction over the (tribe’s) lands,” the tribe said in a court filing. “The court should also afford substantial deference to the thorough and well-reasoned opinions of the United State Department of the Interior and the Indian Gaming Commission that reach these same conclusions.”

The Wampanoags want to offer electronic, high-stakes bingo-style games that can often resemble slot machines found in traditional casinos. They don’t propose offering casino table games, like blackjack, craps and roulette.

The state counters that the tribe specifically forfeited the right to offer gambling when it reached a settlement with Massachusetts for those lands in 1983. The agreement stipulates that the tribe was subject to local and state laws in effect at the time. It was subsequently approved by state lawmakers and Congress.

“Federal legislation codifying the settlement agreement expressly applied ‘those laws and regulations which prohibit or regulate the conduct of bingo or other games of chance’ to the settlement land,” the state said in legal briefs.

The suit was filed in December 2013; Massachusetts is joined by the town of Aquinnah and a local community association in suing the tribe. Each side has asked the judge to decide the case on the arguments rather than take it to trial, and a hearing is set for Aug. 12 in Boston.

Buddy Vanderhoop, an Aquinnah Wampanoag, says the gambling debate has also divided tribal members. Most of those living on the island are opposed to the plan while mainland members are largely supportive, he says.

The tribe has about 1,200 members. Most live on the mainland in New Bedford and other southeastern Massachusetts cities.

“We’re outnumbered by the tribal members that don’t live here,” Vanderhoop says. “Nobody on this island wants it. It’s all the members in New Bedford. They don’t want it in their backyard.”