Nicolás Maduro has belittled the hundreds of thousands of Venezuelans fleeing across the Andes as gullible “slaves and beggars” duped into scrubbing foreign toilets by enemies of the Bolivarian revolution.

The United Nations said 2.3 million people, more than 7% of Venezuela’spopulation, have left the country since 2015, with most heading to Brazil, Chile, Colombia, Ecuador and Peru. Half a million have arrived this year in Ecuador alone.

But when Daniel Luquez, an unemployed carpenter, set off from his home in the city of Guanare in July he was not, as Venezuela’s president recently scoffed, chasing “the honeys” of a life abroad. He was fighting for his daughter’s life.

Two-year-old Jolismar was diagnosed with thoracic cancer last year after doctors found a small lump near her heart. On Tuesday, and after an arduous three-week journey across Colombia, her father arrived in the Ecuadorian border town of Tulcán determined to earn the money to support his ailing daughter as she undergoes chemotherapy back in their rapidly unravelling nation.

“Getting here was tough, but I have to battle for my family,” said Luquez, 27, who hitchhiked and hobbled almost 1,200 miles to Ecuador. Six years ago his left leg was amputated as a result of a car crash.

Facebook Twitter Pinterest Daniel Luquez,27, travelled 1,200 miles and is one of more than 500 000 people who have crossed into northern Ecuador this year. Photograph: Tom Phillips/The Guardian

Luquez is one of the more than 500,000 Venezuelans who have crossed into northern Ecuador via Colombia this year as his country’s migration crisis escalates. Regional governments struggle to cope with the humanitarian and political fallout from one of the largest mass migrations in Latin American history.

The exodus appears to have accelerated in recent weeks with almost 43,000 Venezuelans streaming into Tulcán over Rumichaca Bridge in the first 14 days of August alone.

José de la Fuente, the regional head of the UN’s refugee agency, UNHCR, said the number could hit 100,000 by the end of this month. “I don’t think anybody imagined a crisis of this size,” he said.

Andrea Obando, who is leading the humanitarian response for Tulcán’s town hall, said even 50 years of conflict involving Colombian paramilitaries and guerrillas had not pushed so many people across the border.

Maduro, who took power after Hugo Chávez’s death in 2013, has struck a defiant tone after the recent attempt to assassinate him, detaining political foes and vowing to revive Venezuela’s nosediving economy.

“I want the country to recover and I have the formula. Trust me,” he said in a televised address on Friday, announcing a major currency devaluation many economists say will make the situation even worse.

Facebook Twitter Pinterest Crowds of Venezuelan migrants wait to cross into Ecuador on the Rumichaca bridge. Photograph: Tom Phillips Latin America correspondent/The Guardian

But with no hint of the economic or migratory crises easing, Venezuela’s neighbours appear to be losing patience.

Brazil, which has taken in tens of thousands of Venezuelans, briefly sealed its northern border in early August, with regional authorities claiming they could no longer cope. “If we carry on like this, by the end of the year we will have lost control of the city,” warned the mayor of Boa Vista, which is near the border.

On Saturday, angry Brazilians set fire to migrant camps in the frontier town of Pacaraima and forced about 1,200 Venezuelan immigrants back over the border after a restaurant owner was robbed and stabbed – allegedly by Venezuelans. The Venezuelan foreign ministry expressed concern over the attacks and urged Brazil to protect the immigrants and their property. Brazil said it would send extra troops to the Roraima border to counter the unrest.

Earlier this year, Chile and Colombia introduced measures designed to deter Venezuelans from coming, and this week Ecuador and Peru followed suit, announcing they would only admit those with passports, something many lack because of the turmoil back home.

Ecuador’s decision was denounced by activists as unconstitutional and inhumane. But it will please some in Tulcán, a picturesque but economically depressed settlement of about 60,000 residents.

Hundreds of them marched through its streets on Thursday, demanding urgent action from President Lenín Moreno to rescue its economy and slow the influx of Venezuelans , some of whom can be seen sleeping rough and begging in parks and squares.

Facebook Twitter Pinterest Hundreds of locals take to the streets of Tulcán, Ecuador to protest against the arrival of thousands of Venezuelan migrants. Photograph: Tom Phillips Latin America correspondent/The Guardian

“You can help five, 10 or 20 Venezuelans but you can’t help … 10,000,” said Jairo Pozo, a business owner behind the protest, accusing “these Venezuelan gentlemen” of stealing Ecuadorian jobs and wallets.

Marco Sánchez, a 32-year-old demonstrator, said he was disturbed by the presence of “this type of person”, claiming: “Lots of people basically come here come to steal.”

Obando said she was concerned about rising xenophobia and blamed local media for sensationalising a handful of offences committed by Venezuelans. Starving incomers had committed some petty crimes, she said, but added that official figures gave lie to claims Tulcán was in the grip of a crime wave.

She said Ecuador’s “arbitrary” decision to bar passport-less Venezuelans would strand many in Tulcán or push them into the hands of people smugglers. Authorities already knew of 25 smuggling trails around the town, she said: “This is going to skyrocket.”

That Venezuela’s exodus will continue is obvious from the tales of despair that abound on Rumichaca Bridge, where thousands assemble each day en route to a new life and a Jehovah’s Witness volunteer has erected a sign posing the question on everyone’s mind: “When will the suffering end?”

Facebook Twitter Pinterest Yemila Urribarri, a 42-year-old psychologist from Maracaibo who is fleeing to Peru with her 14-year-old son, Jhoel. Photograph: Tom Phillips, Latin America correspondent/The Guardian

Yemila Urribarri, a 42-year-old psychologist from Maracaibo who is fleeing to Peru with her 14-year-old son, said her country was disintegrating. “There are children dying of hunger,” she said, her eyes glazing over with tears.

Andrés Chacin, a 21-year-old politics graduate who was Argentina-bound, said his generation had also lost hope: “Eighty per cent of my friends have already emigrated.”

With Maduro clinging on and Venezuela’s opposition divided, Chacin said he sees international pressure as the only chance of change. “Vladimir Putin will decide [what happens]. Xi Jinping will decide. Latin American governments will decide. Nobody else,” he said.

Others on the bridge had more extreme suggestions. “There’s only one way to solve this: kill him – a bomb on Miraflores,” said Alex Ribero, a gold-miner from Ciudad Bolívar, referring to the presidential palace.

A group of backpackers from Germany and New Zealand looked on in disbelief having unwittingly stumbled into the humanitarian emergency. “I’ve never been part of something like this … I had no idea what we were going to be coming into,” said Ashleigh Mcquarters, a 32-year-old accountant who was among the crowd queuing to enter Ecuador.

Over coffee and cake, now unthinkable luxuries back home, Luquez recalled starting his expedition in July with less than a dollar in his pocket. He crossed into Colombia at the town of Arauquita and initially planned to stay in Bogotá. But he abandoned Colombia’s capital after being accosted by a local resident who told him “venecos”, a derogatory word for Venezuelans, were not welcome.

Facebook Twitter Pinterest Daniel Luquez in Tulcán. Photograph: Tom Phillips Latin America correspondent/The Guardian

On his crutches, Luquez hitched and hiked his way south through Cali, over Ecuador’s border and finally to Tulcán where he sells sweets on street corners from 7am to 7pm to help pay for his daughter’s treatment.

“It’s hard. You go three or four days without washing … and if you do take a bath it’s in a river … I never thought I’d go through something like this. I never thought I’d have to leave my country,” he said. “Never.”

That night Luquez retired to the shabby $50-a-month hostel where he has rented a room with help from an international charity. He logged on to its wi-fi network and typed a message into his phone.

“My family is the most important thing to me,” it read. “You don’t know how much I wish they were here with me.”