U.S. Homeland Security Secretary Alejandro Mayorkas said border patrol agents have seen a 50% drop in the number of migrants crossing the border since Thursday, when President Joe Biden's administration shifted to a sweeping new asylum regulation meant to deter illegal crossings.

"The numbers we have experienced in the past two days are markedly down over what they were prior to the end of Title 42," Mayorkas said on CNN's "State of the Union" program. He said there were 6,300 border encounters on Friday and 4,200 on Saturday, but cautioned it was still early in the new regime.

Mayorkas credited the criminal penalties for migrants who illegally enter the country, which resumed under existing law after Title 42's expiration, for the decrease in crossings. The COVID-era rule adopted under former President Donald Trump allowed officials to expel migrants quickly without an asylum process but did not impose penalties.

Biden, asked during a bike ride near his vacation home in Rehoboth Beach, Delaware, how he believed the border situation was going, responded: "Much better than you all expected."

Biden said he did not have plans to visit the border in the near term.

The Biden administration plan requires migrants to schedule an immigration appointment through an app or seek protection from countries they passed through on their way to the U.S. border. If they do not follow the process and are caught entering the U.S. illegally, they are not allowed to try again, even through legal means, for five years. There are prison terms for other violations.

"There is a lawful, safe and orderly way to arrive in United States. That is through the pathways that President Biden has expanded in an unprecedented way, and then there's a consequence if one does not use those lawful pathways," Mayorkas said.

Officials from communities along the border agreed they had not seen the large numbers of migrants that many had feared would further strain U.S. border facilities and towns.

"The amount of migrants we were expecting initially - the big flow - is not here yet," Victor Trevino, mayor of Laredo, Texas, told CBS News' "Face the Nation."

But Republicans who control the U.S. House of Representatives warned a surge could still be on the way.

"I do think there are caravans going up. I think they still want to get in," Representative Michael McCaul said on ABC's "This Week" program.

Representative Mark Green, Republican chairman of the House Homeland Security Committee, told CNN: "What the secretary failed to say is, this week has seen more crossings than any time, any week, in our history."

Mayorkas defended the Biden administration policy against a lawsuit by the American Civil Liberties Union that claims the restrictions violate U.S. laws and international agreements.

"This is not an asylum ban. We have a humanitarian obligation, as well as a matter of security, to cut the ruthless smugglers out," he told ABC.

'BROKEN' IMMIGRATION SYSTEM

With U.S. immigration policy in disarray, holding facilities, hospitals and towns have been left to struggle after tens of thousands of migrants waded through rivers and climbed walls and embankments onto U.S. territory last week in the days before Title 42 expired.

Trevino said hospitals were at or near capacity, with no pediatric intensive care unit available and an emergency declaration in effect.

El Paso Mayor Oscar Leeser told CBS that the Red Cross was helping private organizations and church groups provide food and other assistance for migrants.

"The immigration process is broken. There's no ifs ands or buts about it. But we are getting the resources that we need," Leeser said.

There has been little movement toward a bipartisan agreement to address immigration in Congress.

Just before Title 42 expired on Thursday, House Republicans approved legislation that would resume construction of a border wall, expand federal law enforcement efforst and require asylum seekers to apply for U.S. protection outside the country.

The Republican bill is unlikely to be taken up by the Democratic-controlled Senate.