VENEZUELANS, ONCE the richest people in Latin America, are living through an extraordinary humanitarian catastrophe. Deprived of adequate food, medicine, power and water, subjected to a terrifying epidemic of violent crime, ruled by a repressive, corrupt and monumentally incompetent government, they are fleeing their country at the rate of an estimated 5,000 per day. Not only have they received scant aid, but Latin American nations and the regime of Nicolás Maduro are taking steps that will make their suffering even worse.

On Friday, Mr. Maduro, an economic illiterate who has overseen a drop of nearly 50 percent in Venezuela’s economic output, announced a drastic but incoherent package of measures intended to stop the free fall. It included some conventional steps the government has resisted for years, such as a huge devaluation and a promise to raise some gasoline prices to international levels. But they were accompanied by other measures, such as a 30-fold increase in the minimum wage, that are likely to accelerate an inflationary storm that is already measured in the tens of thousand percent.

Some experts believe that what remains of economic activity may seize up altogether. Opposition leaders have called a general strike, but the regime has proved adept at putting down popular uprisings by force. For a growing number of Venezuelans, the only alternative is to follow the more than 2 million of their fellow citizens — out of a population of 32 million — who have already sought refuge in other countries, including the United States.

The movement of refugees is described by U.N. officials as one of the largest in Latin American history. More than 1 million are believed to be in Colombia, 600,000 have crossed into Ecuador this year, and 400,000 are in Peru. More than 70,000 have sought U.S. asylum, making Venezuela by far the largest source of asylum seekers. Its Latin American neighbors, along with Caribbean nations such as Trinidad and Tobago, lack the resources to manage the Venezuelans, many of whom are destitute and desperate. Many have been victimized by human traffickers and other criminals. Yet the international response has been anemic: The U.N. refu­gee agency had raised only half of the $46 million it was seeking for Venezuela operations as of early August.

Now several governments are taking steps to block Venezuelans seeking refuge. Ecuador and Peru announced last week that they would admit only those carrying passports, which are nearly impossible to obtain in Venezuela. Chile already imposed such a restriction. The Brazilian government meanwhile announced it would send troops to the border state of Roraima, where Venezuelan migrants were attacked by a mob on Saturday.

The U.S. response has also been disappointing, despite frequent condemnations of the Maduro government by President Trump, Vice President Pence and other officials. The administration has provided $12 million to U.N. refu­gee efforts and about $55 million overall; Defense Secretary Jim Mattis said last week that a Navy hospital ship would be stationed off Colombia to provide medical aid to Venezuelans.

That’s not adequate. While the United States cannot easily force a political change in Caracas, it can at least do much more to help refu­gee Venezuelans and the nations hosting them. Otherwise, it risks allowing the disaster in one nation to become a regional crisis.