WASHINGTON - President Joe Biden said Thursday the U.S. would immediately begin turning away Cubans, Haitians and Nicaraguans who cross the border from Mexico illegally, his boldest move yet to confront the arrivals of migrants that have spiraled since he took office two years ago.

The new rules expand on an existing effort to stop Venezuelans attempting to enter the U.S., which began in October and led to a dramatic drop in Venezuelans coming to the southern border. Together, they represent a major change to immigration rules that will stand even if the Supreme Court ends a Trump-era public health law that allows U.S. authorities to turn away asylum-seekers.

“Do not, do not just show up at the border,” Biden said as he announced the changes, even as he acknowledged the hardships that lead many families to make the dangerous journey north.

“Stay where you are and apply legally from there,” he advised.

Biden made the announcement just days before a planned visit to El Paso, Texas, on Sunday for his first trip to the southern border as president. From there, he will travel on to Mexico City to meet with North American leaders on Monday and Tuesday.

The first night under the new restrictions got off to an eerily quiet start in Yuma, Arizona, where hundreds of migrants usually cross like clockwork daily between midnight and sunrise, including many Cubans. By 2 a.m. local time Friday, no one had crossed in a popular spot for people to turn themselves in to Border Patrol agents.

A large Border Patrol bus with caged windows, the kind typically used to transport prisoners, sat idle with its motor running along with several white Border Patrol vans on a dirt road where the border wall ends. There was no one under a large white canopy that was erected months ago to shield migrants from the sun as they wait to be driven to a Border Patrol station.

An agent said the low turnout could be a result of the previous day’s announcement but also noted the river was high. He suggested waiting until 5 a.m. Migrants tend to arrive in groups ranging between 200 and 300 people, he said.

Homeland Security officials said they would begin denying asylum to those who circumvent legal pathways and do not first ask for asylum in the country they traveled through en route to the U.S.

Instead, the U.S. will accept 30,000 people per month from the four nations for two years and offer the ability to work legally, as long as they come legally, have eligible sponsors and pass vetting and background checks. Border crossings by migrants from those four nations have risen most sharply, with no easy way to quickly return them to their home countries.

“This new process is orderly,” Biden said. “It’s safe and humane, and it works.”

The move, while not unexpected, drew swift criticism from asylum and immigration advocates, who have had a rocky relationship with the president.

“President Biden correctly recognized today that seeking asylum is a legal right and spoke sympathetically about people fleeing persecution,” said Jonathan Blazer, the American Civil Liberties Union’s director of border strategies. “But the plan he announced further ties his administration to the poisonous anti-immigrant policies of the Trump era instead of restoring fair access to asylum protections.”

Even with the health law restrictions in place, the president has seen the numbers of migrants crossing the U.S.-Mexico border rise dramatically during his two years in office; there were more than 2.38 million stops during the fiscal year that ended Sept. 30, the first time the number topped 2 million. The administration has struggled to clamp down on crossings, reluctant to take hard-line measures that would resemble those of the Trump administration.

That’s resulted in relentless criticism from Republicans who say the Democratic president is ineffective on border security, and the newly minted Republican House majority has promised congressional investigations on the matter.