- Several people in the town of El Paso in Texas said they hurried to reach the border ahead of the policy change.
- They told the BBC they were unsure what the new rules would mean and had been left confused by rumours and misinformation.
Tens of thousands of people are waiting to cross into the US from Mexico, officials say, after a pandemic-era border policy expired on Friday.
The policy, known as Title 42, allowed the US to swiftly deport people without an asylum hearing, using the coronavirus pandemic as justification.
It ended overnight after three years along with the country's national Covid-19 health emergency.
President Biden's new rules to replace Title 42 are facing legal challenges.
Several people in the town of El Paso in Texas said they hurried to reach the border ahead of the policy change. They told the BBC they were unsure what the new rules would mean and had been left confused by rumours and misinformation.
Jon Uzcategui and his girlfriend Esmaily, both 24, arrived here from Venezuela. They said they were told by smugglers and other migrants that they would be immediately deported if they presented themselves at the border, prompting them to illegally cross the barriers separating El Paso from Mexico.
"We trusted them, and were starting to move into the US. But we were stopped at a roadblock," said Mr Uzcategui, who was eventually allowed in after his asylum claim was heard. "The agents told us that [what we heard] was all false."
"All the migrants were talking about 11 May," he added. "But there were lots of rumours. We just knew something was changing."
The end of Title 42 triggered a desperate race to the 2,000-mile (3,200km) US-Mexico border. About 10,000 people have been crossing each day - the highest levels on record.
Border authorities on Friday said they had not seen "a substantial increase" in migrants crossing since the end of Title 42.
The Mexican government put the number of waiting migrants at its border with the US at just under 27,000 - less than half of the US estimate of 60,000.
Ahead of the policy's expiration, it was quiet in El Paso where makeshift migrant camps on the city's streets have largely been removed. But local authorities and humanitarian organisations are bracing for what some fear may be a difficult-to-manage rise in attempted crossings.
The city's mayor, Oscar Leeser, warned that an estimated 10,000 migrants were waiting for an opportunity to cross into El Paso from Ciudad Juarez in Mexico.
The Biden administration has unveiled a raft of new measures aimed at encouraging people to stop crossing illegally and to follow the asylum process.
These include the opening of regional processing centres in Latin America and the expanded use of a Customs and Border Patrol-run app to book asylum appointments.
Officials say those crossing the border illegally will be deported, barred from re-entering the US for at least five years and presumed ineligible for asylum.
Under Title 42, there were no such consequences meaning repeat attempts to cross the border were common.
"We are ready to humanely process and remove people without a legal basis to be in the US," Homeland Security Secretary Alejandro Mayorkas said. "The border is not open."
The new rules and the efforts of immigration officials to assuage the fears of local residents have done little to reassure many of those who help migrants in El Paso.
"It's going to be a very large challenge for us," said Susan Goodell, the chief executive of El Pasoans Fighting Hunger Food Bank, which has been feeding hundreds of migrants each day on the city's streets.
"We're preparing, to the best of our ability, to find the food that we need to feed people living on the street or in shelters," she said. "With the lifting of Title 42, we think it'll be a short time before we start seeing a large number of migrants coming into the community again."
"We're stocking up on food and supplies as much as possible," said Nicole Reulet, marketing director of Rescue Mission El Paso, a local shelter that houses migrants.
"Nobody really knows what to expect, or what the numbers will look like. It makes it hard for us to prepare."
On Thursday, about 25,000 migrants were in Border Patrol custody, far exceeding the agency's capacity to hold them.
To reduce overflow, officials had planned to release migrants and tell them to report to an immigration office within 60 days. That effort, however, was blocked by a federal judge in Florida. The Biden administration is expected to appeal.
In the longer term, the lifting of Title 42 is likely to be a contentious political issue in the US. House Republicans, for example, are already considering a package of immigration bills, although they have little chance of passing a Democratic-controlled Senate.
The country's immigration system has not been significantly updated for decades and both Democrats and Republicans have said it is in need of reform.
But the two sides have major differences on border policy, meaning there is little prospect of bipartisan legislation that could overhaul the system in future.