Thousands of asylum seekers have converged on the US border with Mexico, anticipating the lifting of pandemic-era restrictions, but there is no clear indication of what the process might be to enter the United States.

Asylum seekers are unclear if they should show up at a border crossing with Mexico and ask a US official for asylum, sign up online, go to a US embassy or consulate or what their next steps should be.

US President Joe Biden’s administration has been conspicuously silent about how asylum seekers should enter the United States when asylum limits put in place by his predecessor, Donald Trump, end, generating rumours, confusion and doubts about the government’s readiness despite more than two years to prepare.

“I absolutely wish that we had more information to share with folks,” said Kate Clark, senior director for immigration services at Jewish Family Service of San Diego, which has facilitated travel within the United States for more than 110,000 migrants released from custody since October 2018.

People have been denied rights to seek asylum under US and international law 2.5 million times since March 2020 on grounds of preventing COVID-19 under Title 42, a public health rule that was scheduled to expire on Wednesday until US Supreme Court Chief Justice John Roberts ordered a temporary hold.

Title 42 has been applied disproportionately to those from countries that Mexico has agreed to take back: Guatemala, Honduras, El Salvador and more recently Venezuela, in addition to Mexico. People from those countries are expected to drive an anticipated increase in asylum claims once the rule is lifted.

Roberts asked Biden administration to respond to the stay by 5pm (22:00 GMT) Tuesday. That’s just hours before restrictions are slated to expire on Wednesday.

The Department of Homeland Security, which is responsible for enforcing border security, acknowledged Roberts’s order — and also said the agency would continue “preparations to manage the border in a safe, orderly, and humane way when the Title 42 public health order lifts”.

Suspense mounted at the US border with Mexico on Tuesday about the future of restrictions on asylum seekers as the Supreme Court issued a temporary order to keep pandemic-era limits on migrants in place.

Conservative-leaning states argued in their appeal to the Supreme Court that an increased number of asylum seekers would take a toll on public services, such as law enforcement and healthcare, and warned of an “unprecedented calamity” at the southern border.

In El Paso, Democratic Mayor Oscar Leeser had warned Monday that shelters across the border in Ciudad Juarez, Mexico are packed to capacity with an estimated 20,000 migrants who are prepared to cross into the US.

Despite the court stay Monday, the City of El Paso rushed to expand its ability to accommodate more migrants by converting large buildings into shelters, as the Red Cross brings in 10,000 cots.

Local officials also say they hope to relieve pressure on local shelters by chartering buses to other large cities in Texas or nearby states, bringing asylum seekers a step closer to relatives and sponsors in coordination with nonprofit groups.

Biden administration officials said they have marshalled more resources to the southern border in preparation for the end of Title 42. That includes more border patrol processing coordinators, more surveillance and increased security at ports of entry.