ALBANY – Leaving the Seneca Nation on its own, the second of three Native American tribes on Tuesday cut a deal with Gov. Andrew M. Cuomo that will restrict the state from locating any new casinos in a vast region surrounding Indian-owned gambling halls.

The St. Regis Mohawks, operators of a casino near the Canadian border north of Watertown, will not have to worry about any new competition in a sprawling eight-county region of the North Country if Cuomo, lawmakers and voters approve a casino expansion plan for the state.

Cuomo announced the deal at the Capitol with two Mohawk chiefs Tuesday, one week after cutting an agreement with the Oneida Indian Nation that will let it continue to run its Turning Stone Casino in Central New York without worrying about new gambling competition.

The Senecas and Cuomo, though, are far apart in resolving a dispute that began during the administration of former Gov. David A. Paterson.

The Senecas owe the state and local governments in Western New York about $600 million in slot machine revenues from three Seneca casinos. Cuomo wants that debt paid in return for providing a guarantee that the state will not let any other casinos into the region. Last week, Seneca President Barry Snyder Sr. called Cuomo’s negotiating tactics “childish”’ and accused him of engaging in “schoolyard bullying tactics.”

Cuomo said he had not heard Snyder’s comments and would offer no response. The governor has threatened to try to place a casino in Niagara Falls near the tribe’s facility if the Senecas do not come to terms with the state. Last week, he suggested the tribe’s three Western New York casinos could close in 2016 when its gambling compact with the state expires.

Cuomo has proposed that three non-Indian casinos be allowed upstate as part of a broader referendum that voters could consider this fall legalizing up to seven such casinos. He has divided upstate into six regions eligible for casinos.

The Mohawks, like the Senecas, complained that new gambling came into their exclusivity zones, violating their compact with the state and ending the requirement that they share 25 percent of slot machine revenues with the state.

The Mohawks and the state in the coming months will negotiate a deal to permit the tribe to expand its territorial area in northern New York. The Mohawks will pay back $30 million of the $60 million they have withheld since 2010.

Asked if the Mohawk deal means he is willing to accept less money than the $600 million the Senecas owe the state, Cuomo said the two situations are “totally different.”

The Seneca Nation did not comment.