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“Just fix it. Just decide what are we, and having clear rules will sort everything out,” he said.

He supports statehood but says his promise to voters was to push for a process that will let voters decide once and for all.

He’s asking Congress to pass a bill that would put up two referendums. The first would ask if Puerto Rico’s residents want to change their status, and the second, which would come later if voters say they want a change, would ask if voters want independence, free association with the U.S. or statehood.

Mr. Obama, during last year’s campaign, promised to support Puerto Rico’s efforts to have its status resolved. Mr. Fortuno said he hopes the White House will announce its support for the process once a bill passes the U.S. House — which the governor hopes could happen this year.

If Puerto Rico were to become a state, it would likely gain six seats in the U.S. House as well as two senators.

But Mr. Fortuno was less certain the residents of the District should see the same fate.

“It’s an interesting argument, and out of commity to my colleague from the District, I said, I support you in general, but I don’t think that’s the answer to it,” he said. He said the residents of the city could have representation in Maryland or Virginia as a solution short of statehood. “It has to be fixed. I feel there could be many ways to fix it.”

As for the territory’s economy, Mr. Fortuno says it went into recession three years before the United States as a whole. He’s battling poor credit ratings for Puerto Rico’s bonds and has had to impose what he calls temporary taxes on cigarettes and alcohol — though he says he’ll never support an income- or sales-tax increase.

Mr. Fortuno is a member of both the Republican Party and the New Progressive Party, which is one of two main parties that vie for political offices in Puerto Rico.

Jennifer Haberkorn contributed to this article.