A first group of 25 asylum seekers crossed the US border on Friday under President Joe Biden's sweeping immigration reforms, while thousands more waited in Mexico hoping that they, too, would be allowed in.

Under former president Donald Trump's "Remain in Mexico" programme, tens of thousands of non-Mexican asylum seekers — mostly from Central America — were sent back over the border pending the outcome of their applications.

Biden's administration moved quickly to start dismantling the controversial policy, officially called the Migrant Protection Protocols (MPP), with a first stage that began on Friday.

A group of 25 migrants crossed the border by bus from the Mexican city of Tijuana accompanied by representatives of UN refugee agency UNHCR, according to an AFP journalist.

A shelter official in San Diego, who asked not to be named, later confirmed that they had arrived at a hotel there, although their final destinations were unknown.

The American Civil Liberties Union welcomed their arrival as "an important step in rebuilding" the US asylum system.

"But thousands are still suffering right now stuck in limbo under this inhumane policy," ACLU San Diego spokesman Edward Sifuentes said.

"We urge the administration to quicken the process to safely welcome all people who suffered under MPP. For the families who have been forced to live in danger, there is no more time to wait."

According to the US Department of Homeland Security (DHS), there are approximately 25,000 active cases. Mexico says 6,000 remain on its territory.

Candidates are tested for the coronavirus before crossing, a senior DHS official said.

Only those who have begun the process of applying for asylum will be considered for entry.

Tensions were high on the border as migrants waited to see if they would be allowed to cross over.

"Nobody knows anything. There’s tension. Stress is mounting,” Cuban lawyer Joel Fernandez said.

The 52-year-old crossed 11 countries to arrive in January 2020 in a camp in Matamoros across the border from Texas where he is staying with hundreds more migrants.

"I’ve withstood all the tests that God put in front of me on this difficult journey,” he said.

"Now I want the prize: to have my residency, to work, to bring my wife, my children.”

‘Can’t go back’

In Tijuana, hundreds of migrants spent the night next to the border fence hoping to be allowed in.

But most recognised that they had not yet initiated an asylum procedure.

"The truth is I don’t have an appointment,” said Haitian migrant Geraldine Nacice, who has family waiting for her in the United States.

"I can’t go back to my country any more. There’s war in Haiti right now,” she said, referring to the political turmoil shaking her country.

The "Remain in Mexico” programme was part of Trump’s hardline plan to fight undocumented immigration, along with the construction of a border wall and a policy which separated children from thousands of migrant families.

After Biden took office on January 20, his administration announced that it would reverse the most controversial measures.

On Thursday, Biden’s Democrats unveiled legislation for his plan to create a path to citizenship for 11 million undocumented immigrants already living in the United States.

In the Mexican border city of Ciudad Juarez, a 37-year-old who fled domestic abuse in El Salvador with her four children said she was optimistic things would get better under Biden.

The woman, who asked not to be named for safety reasons, had a US court hearing in December 2019.

But the pandemic and Trump’s tough immigration policies mean her asylum case has seen little progress.

Her dream is for her children to have a good education.

"It’s hard to tell your children that everything is going to be fine when you feel like the world is crashing down on you,” she said.