KEY WEST, Fla. (AP) — Yoandri Sánchez Sánchez arrived in the Florida Keys just before sunrise Thursday with 22 other Cubans on a makeshift, motorized raft they built themselves.

Their 100-mile (160-kilometer) journey from the communist island across the dangerous Florida Straits began on New Year’s Eve and was interrupted by heavy rain that forced them to take shelter on a small deserted island for a couple days. But after six days they finally made it, and Sanchez was overcome with joy.

“We came to work and to help our families in Cuba,” said Sánchez, who is among more than 4,400 migrants, mostly Cubans with some Haitians, who have arrived by boat in Florida since August as those two countries face deepening and compounding political and economic crises. Amid the influx in Florida and a much bigger one in Texas, the Biden administration announced new immigration rules Thursday.

Sánchez was waiting to receive documents at a Border Patrol office in the Keys that will allow him to enter the U.S. and work — at least for now. Because Washington and Havana don’t have diplomatic relations, there is no way for the U.S. government to send him and other Cubans back. He has family in Florida who can help him, but he left behind his parents, his wife, two brothers and two grandsons.

“What matters is that we are already here,” said Sánchez, who began crying.

Just hours after Sánchez and his group arrived, President Joe Biden signaled a tougher stance on migrants coming from Cuba, Haiti and Nicaragua, saying it would immediately start turning people from those countries who who cross the U.S.-Mexico border illegally, as it has done with Venezuelans. However, it was not immediately clear what impact this would have on migrants who arrive in Florida.

Those who are stopped at sea are already taken back — Cuba will accept those. Almost 8,000 Cubans and Haitians have been interdicted since August — about 50 per day compared with 17 per day in the 2021-22 fiscal year and just two per day during the 2020-21 fiscal year. Officials said at least 65 migrants have died at sea since August.

Over the New Year’s weekend alone, more than 700 migrants, mostly Cubans, arrived in the Keys , including 337 who landed on the remote islands that compose Dry Tortugas National Park. They were taken Thursday by Coast Guard cutter 70 miles (110 kilometers) to the Keys for processing.

Florida officials have appealed to the U.S. government to do more to deter migrants from making the risky trek.

Monroe County Sheriff Rick Ramsay, whose jurisdiction is most of the 180-mile (290-kilometer) Florida Keys island chain, said the influx is taxing his 194-deputy department and he wants the Democratic president and his administration to do more.

“I’m experiencing about 10 migrant loads per day in my small county, which for me, resources wise, is very challenging,” Ramsay said at an event Wednesday sponsored by U.S. Sen. Rick Scott. “I’m sympathetic for the migrants who come here — I want them to have a happy life. But we have to have a plan.”

Scott, a Florida Republican, said the U.S. is experiencing “a border crisis.”

Coast Guard Rear Adm. Brendan McPherson said in a statement late Wednesday that despite the increase, “the southeast maritime border is not open.” He asked Cuban and Haitian Americans “to discourage family members in Cuba or Haiti from attempting the dangerous and very often deadly voyage.”

Florida Gov. Ron DeSantis, a Republican who used state tax dollars to fly Venezuelan asylum seekers from Texas to Massachusetts to protest Biden’s immigration policies, has not said anything this week about the Keys situation. His press office did not respond to email requests for comment Wednesday and Thursday.

Ramón Raul Sanchez with the Cuban-American group Movimiento Democracia said the Biden administration’s new policy is like “trying to use a broken umbrella to not get rained on.” He said the real problem is the Cuban government, whose actions prompt Cubans to flee their country. Now he said he worries even more Cubans may risk their lives by taking to the sea to reach the U.S. instead of flying to Central America and coming by land.

That’s how most Cubans attempt to enter the U.S. In the 2021-22 fiscal year, 220,000 Cubans were stopped at the U.S.-Mexican border, almost six times as many as the previous year.

As part of its new policy announced Thursday, the U.S. government said it will accept 30,000 people per month from Cuba, Haiti, Nicaragua and Venezuela who arrive legally, have eligible sponsors and pass background checks.

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Spencer reported from Fort Lauderdale, Florida. Salomon reported from Miami.