NASHUA, New Hampshire — Marco Rubio has made his Cuban heritage and opposition to the Cuban government’s abuses central themes in his presidential pitch, but on Thursday he sharpened his tone on Cuban immigrants to the U.S., saying the influx of Cubans to the U.S. is “becoming a real crisis.”

Speaking at a house party in Bedford, New Hampshire, Rubio said that he’s taking action within the next week to reign in some benefits for Cubans who flee to the U.S. Later that day, he said that the influx of thousands of Cuban immigrants expected to the U.S. In the coming months constitutes a “crisis” and shouldn’t be allowed in.

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In Bedford, Rubio outlined the “issue” in Florida posed by the fact that “Cubans have a special status.” He noted that Cubans who immigrate to the U.S., “a year and a day later, no matter how you came, you are allowed to become a resident,” and go on to abuse Social Security by moving back home and bringing the U.S. Government funds back with them.

“We have people living in Cuba off Social Security benefits. They never worked here,” he said. “This is an outrageous abuse, and I have a law that we are going to introduce this week that shuts down this issue. It’s wrong.”

Rubio’s staff didn’t offer further details on the bill Rubio plans to offer, and said only that details would come next week. But it’s likely to address the Cuban Adjustment Act, the 1966 law that offered fast-track status to U.S. Citizenship and other benefits to Cuban immigrants. Rubio said during the 2013 immigration reform debate in the Senate that the law should be “re-examined,” and in November of this year told the Associated Press that it was a “legitimate point” to ask why Cuban immigrants get special status.

A recent Sun Sentinel investigation found that Cuban immigrants receive more than $680 million a year in welfare, and documented many cases in which Cuban immigrants return back home shortly after receiving citizenship and benefits in the U.S.

Two House Republicans have offered legislative fixes for the issue — one, from Arizona Rep. Paul Gosar, would repeal the Cuban Adjustment Act entirely, while another, from Florida Rep. Carlos Curbelos — a Cuban-American himself — wouldrequire Cuban immigrants to prove they’re political refugees before they’re offered public assistance.

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On Thursday, Rubio hinted he might go even further, again telling reporters after a town hall in Nashua that “we need to reexamine” the Cuban Adjustment Act “and make changes to it based on new realities but also the benefits people are qualifying for.”

“You now have evidence of people are coming to the U.S. under the Cuban adjustment act, they’re qualifying for social security or other benefits and they’re moving back to Cuba and they’re collecting the checks there and that’s just outrageous,” he said.

Rubio also said that the estimated 8,000 Cubans that could migrate to the U.S. Following a deal worked out by a handful of Central American countries last week to allow them out of Costa Rica shouldn’t be allowed in the U.S.

“I think at this point, the migratory policy with Cuba has changed dramatically. You’ve seen a huge upsurge [in immigration] now after the deal with president made with the Castro brother [to thaw relations] and it’s becoming a real crisis,” Rubio said.

“This notion that you’ll have people coming up Central America and into the United States through the southern border is unacceptable.”

This article first appeared on NBCNews.com.