– Hundreds turn up each day, many arriving penniless and gaunt as they pass a tattered flag that signals they have reached the border.

Once they cross, many cram into public parks and plazas teeming with makeshift homeless shelters, raising concerns about drugs and crime. The lucky ones sleep in tents and line up for meals provided by soldiers — pregnant women, disabled people and families with young children are often given priority. The less fortunate huddle under tarps that crumple during rainstorms.

The scenes are rem­iniscent of the waves of desperate migrants who have escaped the wars in Syria and Afghanistan. Yet this is happening in Brazil, where a relentless tide of people fleeing the deepening economic crisis in Venezuela has begun to test the region’s tolerance for immigrants.

This month, the governor of the northern Brazilian state of Roraima sued the federal government, demanding it close the border with Venezuela and provide additional money for her overburdened education and health systems.

“We’re very fearful this may lead to an economic and social destabilization in our state,” said the governor, Suely Campos.

The tens of thousands of Venezuelans who have found refuge in Brazil in recent years are walking proof of a worsening humanitarian crisis that their government claims does not exist.

They also constitute an exodus that is straining the region’s largely generous and permissive immigration policies. Earlier this month, Trinidad deported more than 80 Venezuelan asylum-seekers. In Colombian and Brazilian border communities, local residents have attacked Venezuelans in camps.

During the early months of this year, 5,000 Venezuelans were leaving their homeland each day, according to the United Nations.

If the rate remains steady, more than 1.8 million Venezuelans could leave by the end of this year, joining the estimated 1.5 million who have fled the economic crisis to rebuild their lives abroad.

As Venezuelans began resettling across Latin America in large numbers in 2015, for the most part they found open borders and paths to legal residency in neighboring countries.

But as their numbers have swelled — and as a larger share of recent migrants arrive without savings and in need of medical care — some officials in the region have begun to question the wisdom of open borders.

Campos said she took the “extreme measure” of suing the federal government because the influx of Venezuelans led to a spike in crime, drove down wages for menial jobs and set off an outbreak of measles, which had been eradicated in Brazil.

At least 93 people were killed during the first four months of this year, already exceeding the 83 violent deaths recorded last year, Campos said. And law enforcement officials say drug trafficking in the region has increased as destitute Venezuelans have been drafted into Brazilian smuggling networks.