A county thousands of miles from the U.S. border with Mexico in New York state has declared a state of emergency after officials in New York City said they would begin sending asylum-seeking immigrants there to ease the growing pressure on America’s largest city.

The executive in charge of Rockland County, just north of New York City, Ed Day, said Saturday his office has passed an emergency resolution — in effect for 30 days — preventing other municipalities from sending immigrants his way and forbidding hotels from housing those immigrants without licenses.

“This is absurd, and we will not stand for it,” Mr. Day said. “There is nothing humanitarian about a Sanctuary City sending busloads of people to a County that does not have the infrastructure to care for them. It’s the same as throwing them in the middle of the ocean with nowhere to swim.”

His comments come just one day after New York’s mayor, Eric Adams, said his city was preparing a plan to send hundreds of single adult men to hotels in the towns of Orangeburg in Rockland County and Orange Lake in neighboring Orange County.

Mr. Adams’ said his measures are aimed at making room in New York shelters for the thousands of migrants expected to pour into the city when a pandemic-era policy known as Title 42, which allows U.S. officials to immediately deport asylum-seekers attempting to enter the country, expires on Thursday.

Officials in Orange County tell News 12 Westchester that the plans to house the migrants in their county has already been put on hold by Mr. Adams, but the plans to send 340 men to Rockland County remain on track despite the protests of local officials. “Mayor Adams said that he would hold off on sending a bus to Newburgh, but did not offer a timetable,” said the city supervisor of Newburgh, Gil Piaquadio said. “We need questions answered about zoning, logistics, and who the individuals actually are.”

In an angry post on the Rockland County government’s Facebook page, Mr. Day promised daily fines of up to $70,000 and potential arrests of anyone violating the terms of the newly passed state of emergency. “Extreme actions warrant extreme measures. I warned the NYC Mayor that if you try to run us down we will reach up and grab you by the throat,” he said. “I promised that Rockland would not yield so here we are. No wavering and no retreat.”

New York City has been struggling with a massive influx of migrants — some sent to the city by Republican governors in border states such as Texas — in recent months that is only expected to get worse in the coming weeks. Officials said Friday that there are currently more than 37,500 migrants being housed in New York shelters, the highest in the city’s history. Some 60,800 migrants have arrived in the city since last spring, the mayor’s office said.

“Despite calling on the federal government for a national decompression strategy since last year, and for a decompression strategy across the state, New York City has been left without the necessary support to manage this crisis,” Mr. Adams said. “With a vacuum of leadership, we are now being forced to undertake our own decompression strategy. This new, voluntary program will provide asylum seekers with temporary housing, access to services, and connections to local communities as they build a stable life in New York state.”

Tens of the thousands of migrants from across the globe have been camped in makeshift shelters on the Mexican side of the border for months awaiting an end to the Title 42 measures. When the policy ends on Thursday, many of them are expected to attempt to cross the border into the United States and ask for asylum. Last week, Mr. Biden said he was sending 1,500 active-duty military troops to the border to assist the Border Patrol with the expected surge.

Speaking on “Fox News Sunday,” Congressman Henry Cuellar, a Democrat representing a border district in Texas’ Rio Grande Valley, said the measures may be too little, too late and that there needs to be repercussions for those who attempt to cross the border illegally. “If you don’t have repercussions at the border, people are going to see the border as a speed bump,” he said. “There’s a way that you can have law and order and still respect the legitimate — and I emphasize the word legitimate — asylum claims.”

The chief of the U.S. Border Patrol, Raul Ortiz, said Saturday his agency apprehended nearly 55,000 illegal migrants at the border last week alone, and that at least 18,000 others evaded capture by law enforcement officials. For the month of March, the last month for which full figures are available, the Border Patrol reported apprehending more than 162,000 migrants.