LIMA, Peru — Two South American nations are stiffening entry requirements for the flood of Venezuelans fleeing their nation’s economic and humanitarian crisis, a move that could make their plight even more arduous.

Authorities in Peru announced Friday that they will follow Ecuador’s recent decision to require Venezuelans reaching the border to enter with a passport, a document that has grown increasingly difficult to obtain in Venezuela.

The decision drew an immediate rebuke from authorities in Colombia, which has become a gateway for hundreds of thousands of Venezuelans leaving their homeland. Many are crossing through the Andean nation on their way to other places in Latin America.

Though his own country already imposed its own often ignored entry requirements for Venezuelans, Colombia Migration Director Christian Kruger warned that the new passport rule in neighboring Ecuador could create a bottleneck at the Rumichaca International Bridge connecting the two countries. Officials estimate over 4,000 Venezuelans crossed from Colombia into Ecuador each day over the bridge earlier this month.

“We are immensely worried about the consequences this might present,” he said.

According to the United Nations, 2.3 million Venezuelans have fled since 2014 as their country reels from hyperinflation and severe shortages of everything from food and medicine to ink and paper for passports.

Over 1 million Venezuelans have arrived in Colombia in less than two years, with many using the mountainous nation as a bridge to Ecuador and Peru, where some believe they will have better luck finding jobs and applying for asylum.

More than a half million Venezuelans have entered Ecuador since January, prompting officials to declare a state of emergency. In Peru, officials recorded more than 5,000 Venezuelan entries on a recent single day.

“The exodus of Venezuelans from the country is one of Latin America’s largest mass-population movements in history,” William Spindler, the spokesman for the U.N. high commissioner for refugees, said earlier this month.

Colombia began requiring Venezuelans to present a passport or border card allowing for short trips into the nation earlier this year. But thousands still sneak in through hundreds of illegal entry points along the 1,370-mile border with Venezuela. Colombian officials recently agreed to provide legal status to 442,000 who participated in a registry for migrants without valid documents.

A border crossing from Venezuela into the Brazilian city of Pacaraima was closed earlier this month after a judge ruled it should be shuttered until a program to relocate Venezuelan refugees could keep pace with the hundreds arriving each day. That decision was later reversed by an appellate court.

Peruvian Interior Minister Mauro Medina said the passport requirement is needed to ensure an orderly migration. “If something happens to them, we have a way to identify them,” he said. “Also, some bad apples – who don’t represent the majority, who are decent people – filter in and police should have the adequate tools to identify them.”