Busloads of asylum seekers dumped at a Greyhound station near the border in El Paso, Texas, over Christmas leave volunteers and shelters scrambling

A lone Christmas tree strung with lights stands near a pile of donated toys in the main hall of El Calvario United Methodist church in Las Cruces, southern New Mexico, a touch of festive cheer for the migrants who find sanctuary there after a long trek to the United States.

It has brought some comfort to a father from Catacamas in the Olancho department of Honduras, who arrived at the church shortly before Christmas with his 17-year-old daughter, escaping destitution and violence in Central America.

“It has been a very difficult journey. What I’ve gone through is something I will never be able to forget,” said the father, who requested anonymity while talking to the Guardian, for his and his daughter’s security. “I’m looking for something better for my children. I’m only asking for an opportunity to survive.”

The pair are far from the home where they began their journey and still many miles from their goal – meeting up with family members who live in Tennessee.

But the church feels like a brief haven. Surprisingly, perhaps, they were dropped directly at the doorstep by the federal Immigration and Customs Enforcement (Ice) agency, in a bus with 25 other migrants, after a week of being held in detention by the US authorities.

Sometimes, churches and shelters get word from Ice that they are bringing people released from detention into the care of family or sponsors in the US. But not always. Chaos broke out over Christmas in the nearby border city of El Paso, Texas, after Ice dumped more than 200 people at the Greyhound bus station there, and planned to bring more. They were told to sleep rough, not bother anyone and figure out for themselves, with no warning or provisions, how to reach relatives, according to local reports.

Local volunteers hurriedly brought food, water and cellphones to help those stranded and bewildered, while area shelters, full to capacity, tried to find places for them to stay.

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Ice has been unceremoniously offloading migrants from overstretched detention facilities, in increasing numbers in recent months. Authorities allow them to stay with US relatives or sponsors while their applications to remain in the US crawl through the system.

“It’s a challenge,” George Miller, the lead pastor at El Calvario, said.

Ice is releasing an average of 2,000 migrants a week just in the area around Las Cruces and the nearby border city of El Paso, Texas.

Numbers began increasing sharply in the summer after the Trump administration started detaining more people caught crossing the border unlawfully, Miller said.

“We’ve been operating at full capacity ever since,” Miller said. “It looks like this trend will continue for a while.”

The church offers cots, a bit of peace and quiet and hot meals, which Miller said those arriving often haven’t had for weeks and sometimes months.

Coordination between local shelters, including El Calvario, and Ice is led by Annunciation House in El Paso, the mission for refugees, migrants and the homeless that was thrust into the headlines recently after giving voice to the father of Jakelin Caal Maquin, the seven-year-old girl from Guatemala who died in US custody days before Christmas, prompting outrage from the United Nations.

The government hastily announced a new policy of medical checks on every migrant child in its custody after a second death, of a Guatemalan boy, eight, over Christmas.

“We run out of space all the time,” said the executive director, Ruben Garcia. “We’re always trying to find more churches … doing all this with the help of volunteers. It’s a lot of work.” They offer beds, food, showers, access to phones – and encouragement amid the chaos. Annunciation House was on the frontline again on Christmas Eve amid the chaos at the Greyhound station.

“The only reason Ice releases these migrants is because they don’t have enough detention facilities for all of the families – if not they would be releasing a lot fewer migrants,” he added.

Facebook Twitter Pinterest Asylum seekers board a bus after they were dropped off by Ice officials at the Greyhound bus station in El Paso late on 23 December. Photograph: Paul Ratje/AFP/Getty Images

The churches and non-profits the Guardian spoke with asserted that they were not paid by the government; they began coordinating with Ice principally to prevent people ending up on the streets after the government began releasing large numbers, citing a lack of capacity and legal limits on detention.

“I’ve never seen anything like this … the mass releases are unprecedented,” said Teresa Cavendish, director of operations for Catholic Community Services of Southern Arizona, who has been helping asylum seekers in Tucson.

A shelter in Tucson called The Inn, run by pastor Dottie Escobedo-Frank, is named for the biblical story of Mary and Joseph resorting to a stable to bring Jesus into the world after there was no room for them at the inn in Bethlehem.

She said the local bus station called the shelter recently about a group of 20 people who were dropped off there by an Ice bus.

“We are grateful that these folks are getting out and are coming to our place instead of being at the bus depot,” Escobedo-Frank said.

While the Trump administration has been focusing on mass migration “caravans” traveling from Central America, with thousands now stuck in limbo in Tijuana, across the border from San Diego, crossings by small groups and individuals have been surging elsewhere, further from the public eye.

US officials in the Rio Grande valley in eastern Texas are apprehending about 680 people a day, compared with fewer than 150 in San Diego daily, Customs and Border Protection (CBP) said.

Raul Ortiz, local CBP acting chief in eastern Texas said few detained there were part of caravans.

When the authorities ask La Posada Providencia, a shelter in San Benito, eastern Texas, to take in migrants they are never turned down, Magda Bolland, the executive director said. However, its 29 beds are not enough.

“Sometimes I come into work and there’s someone sleeping in my office,” she said.

Church leaders in Arizona say Ice has released about 5,000 migrants in the Phoenix area in the last two months and they have had to scramble to find diapers, clothing and food at the last minute.

Magdalena Schwartz, a local pastor, coordinates with Ice several times a day. She tells them which of a dozen local churches have space after Ice shares how many asylum seekers will be released. Some local pastors have recently asked to take a break, citing strained resources.

“It’s overwhelming. We don’t have enough churches,” she said.

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Central Christian church in Mesa, Arizona, has recruited local host families to take in migrants. And Israel Camacho, a pastor at Iglesia Nueva Esperanza, in Mesa, sets up air mattresses.

“Compared to what the people have been experiencing, to be in a warm place with an air mattress and some hot food is like, ‘wow’,” Camacho said.

After a tumultuous year in US immigration policy, many shelters were full over Christmas.

In Tucson, Escobedo-Frank at The Inn summed up: “In most of the main faiths, there are stories of us welcoming the stranger. At this time, we’re trying to live out the Christmas story in real time, here in the desert,” she said.

The Associated Press contributed to this report