Nearly 9,000 people made the crossing on Saturday, according to officials, marking one of the highest rates of arrivals in recent months.

Oscar Leeser, the mayor of El Paso, said more than 2,000 people were seeking asylum in the city per day, up from 350-400 as recently as six weeks ago, straining resources and filling up shelters.

Over the past 10 days, the city has worked with the US Border Patrol to provide shelter for 6,500 people, he said.

“The city of El Paso only has so many resources and we have come to … a breaking point right now,” Leeser told a news conference.

The influx of asylum seekers, mostly from Venezuela, Honduras and Haiti, is part of a larger swell of migrants who have travelled dangerous routes on buses and cargo trains to Mexican border towns near the cities of El Paso and Eagle Pass in Texas, as well as San Diego in California. Many are searching for opportunity or escaping hunger, violence or political turmoil in their home countries.

The number of people seeking asylum in the US had plummeted in recent months, following the announcement of new restrictions in May, but the recent dramatic increase has put the Biden administration on its heels again. The city of Eagle Pass has declared a state of emergency to deal with the influx, while democratic mayors and governors are seeking more relief for hosting asylum seekers and Republicans are seizing on the issue ahead of the 2024 presidential election.

Lesser told reporters on Saturday that El Paso plans to open a new shelter. On Saturday, five buses were chartered to take the asylum seekers to New York, Chicago and Denver.

Republican governors in Texas and Florida have been criticised for sending migrants to cities perceived as liberal such as New York and Sacramento. But Leeser, a Democrat, said all of the migrants on the El Paso buses were going voluntarily to the cities of their choice.

Leeser said Biden had been a good partner but added that the overall US immigration system was broken.

Many migrants from Venezuela, he said, lacked transportation to their desired destinations, while El Paso’s shelter houses only 400 people and must also be available to help the homeless. About two-thirds of those crossing into El Paso currently are single men, he said. About 32 percent are families and 2 percent are unaccompanied children.

“I think it’s really important to note that we have a broken immigration system,” he said. “It’s the same thing over and over again.”

With tensions rising in Texas, the Biden administration has sent 800 troops to the border, adding to the 2,500 National Guard members there. It has also attempted to stem the migratory flow through special programmes to process asylum and visa requests in migrants’ home countries, pledging consequences for those who do not follow the rules, including deportations and expulsions.

The administration has also extended temporary legal status to an estimated 472,000 Venezuelans who arrived in the US as of July 31, making it easier for them to work in the country.

On Saturday, US Homeland Secretary Alejandro Mayorkas met with Honduran President Xiomara Castro in the city of McAllen in Texas to discuss a bilateral strategy to curb migration.

Mayorkas pledged to crack down on those who fail to use designated pathways to enter the US and said Castro’s leadership was critical to disrupting smuggling networks.

“Together, we are arresting and prosecuting smugglers, disrupting and dismantling their networks and seizing their assets and funds,” he said in a post on X, formerly known as Twitter.

Castro blamed violence by criminal organisations for the outflow of people from her country.

“I believe that in our history, we have never seen an exodus of entire families from our country, seeking opportunities, due to the levels of violence,” she told Mayorkas.

I am grateful to @XiomaraCastroZ for joining me to visit @CBP facilities to see our team’s extraordinary work in action. (1/3) pic.twitter.com/UXflMxMSAn

— Secretary Alejandro Mayorkas (@SecMayorkas) September 23, 2023

In the city of Eagle Pass, which declared a state of emergency on Wednesday, US authorities have set up a thicket of barbed wire to deter crossings. A military convoy was seen at the scene on Saturday, closing gaps in the fence made by earlier arrivals.

Several asylum seekers – many of whom have walked thousands of kilometres on foot, passing through the Darien Gap from Colombia to Panama – told the AFP agency that the fence was no obstacle.

Many burrowed through the sand under the wire, or squeezed through, inch by painful inch on Saturday, as soldiers watched on.

“This here is nothing,” said 17-year-old Venezuelan Dileidys Urdaneta. “Because what we have experienced, what we have gone through, is much worse. And what we left behind – don’t even mention it.

“There is no comparison.”

She told AFP she had reached Eagle Pass carrying only her documents, a phone with no battery and the clothes she was wearing – shorts and a sport top.

“Now,” she added, “it can only get better”.