(NewsNation) — Border officials in Florida say they are stretched thin, stressing that since August, more than 4,000 Cuban and Haitian migrants have arrived in the Sunshine State.

This week, authorities closed Dry Tortugas National Park, about 70 miles west of Key West, after 300 migrants landed on the island in one weekend. The remote park is mainly open water with a few small islands. It is only accessible by boat or seaplane.

The National Park Service provided the migrants with food, water and medical care until authorities arrived to take them to Key West. Responders medically evaluated the hundreds of people and took them by boat to Key West on Thursday.

NewsNation spoke to a man who recently arrived in the U.S. from Cuba. He shared cellphone video of his group’s 10-day journey of roughly 90 miles from Cuba to the Florida Keys. He described the emotion and tears when they realized they had made it to the U.S.

Many of the migrants are brought to Border Patrol buildings. Some are sent back to their homes in places such as Cuba and Haiti. Others are picked up by family and friends while they wait for official next steps.

Craig Cates serves as the mayor of Monroe County, which includes Key West. The surge of migrants over the holiday weekend has raised concerns about the Florida Keys as a tourist destination.

“This is a vacation destination. We’re real worried about people seeing this on the news and not wanting to vacation in the Keys because they think we’re being overwhelmed,” Cates said.

Cates told NewsNation that authorities in his county are doing everything they can, but they need more help.

“That being said, it has to be addressed and dealt with in Washington,” Cates said, later adding: “Quit giving them (migrants) the idea that if they come here, they get to stay. They will risk their lives to do that.”

Callan Garcia is an immigration attorney. He said political unrest in places such as Cuba and Haiti is a major driver of the current migrant increase.

“It seems … that it’s more economically driven from Cuba right now,” Garcia said. “Another part of it is the perception that it comes out of the crisis at the Mexican border, where … word is that people are getting in, people are getting the opportunity to apply for asylum.”

While groups of migrants wait to be processed by officials at the local Border Patrol building in the Keys, officials have had to use an overflow space outside. Since October, Border Patrol’s Miami Sector said it has seen the number of migrant encounters go up by more than 400%.

This comes as President Joe Biden says the U.S. will begin turning away Cubans, Haitians and Nicaraguans who illegally cross the border from Mexico.

“Do not just show up at the border,” Biden said when announcing the move. “Stay where you are and apply legally from there.”

Biden said the U.S. will accept 30,000 people per month for two years from four countries. He said the U.S. will offer them the potential to work as long as they come into the country legally, have sponsors and pass background checks.

The president is expected to visit El Paso, Texas, along the border on Sunday.