No government in the Western Hemisphere knows what to do with Venezuelan migrants. Native populations in host countries are growing restless and sometimes xenophobic. Yet all signs point to continued massive flows. The number of Venezuelan emigrants could soon approach the number of Syrians who have fled their country and create a crisis in Latin America comparable to the one that rocked Europe in 2015.

In the first 15 years of Hugo Chávez and Nicolás Maduro’s dictatorship, hundreds of thousands of Venezuelans fled to the U.S., Colombia, Panama, Spain and other countries. At first this was a gradual, mostly upper- and middle-class affair. Then amid Venezuela’s economic and political meltdown in 2014, the exodus accelerated. People from all strata of society started heading for the exits. In the past few years, the collapse of Venezuela has become the hemisphere’s worst humanitarian disaster ever.

Four million Venezuelans live abroad, of whom 2.3 million have left in recent years due to the inhumane conditions at home, according to Human Rights Watch. Colombia, across the western border, has received more than one million; Ecuador, Peru, Chile, Brazil and Argentina each have received hundreds of thousands more. In many cases the migrants have settled temporarily in border towns, overwhelming the local infrastructure. Sometimes tensions have triggered violence: In Pacaraima, an entry point in Brazil, the local population attacked migrant tents in August after an assault on a local restaurant owner.

Latin American countries were quite welcoming at the start of the crisis but have lately started imposing harsh controls on migration. Ecuador and Chile are demanding passports, which are nearly impossible for migrants to get. Chile requires costly police-record certificates. Brazil has mobilized the army in border areas and is turning migrants back outright. Politicians are making the migrants into scapegoats for social grievances. Ricardo Belmont, a candidate for mayor of Lima, recently said the Peruvian government had a secret plan to naturalize one million Venezuelans in exchange for their votes. He added in vulgar language that Venezuelan women looked too shapely to be fleeing hunger.

To end the confusing and arbitrary status of migrants, the region should admit that the migrants are refugees under the 1984 Declaration of Cartagena. It can do so through the Lima Group, a multilateral body set up last year to deal with the Venezuelan crisis. This would normalize the status of migrants and allow them to be incorporated into the economy and society. It would also provide a mechanism to deal with future migrants, who could perhaps be distributed among the participating countries on a voluntary basis.

Under the United Nations Refugee Convention of 1951, only those fleeing political persecution must be granted refugee status. But under the more expansive Cartagena agreement, which 15 Latin American countries have incorporated into their own legislation, Venezuelans fleeing human-rights violations and state collapse clearly deserve asylum.

By refusing to grant Venezuelans refugee status and instead opting for limited, ad hoc measures, Latin American governments claim they are preventing a temporary situation from becoming permanent and avoiding costly commitments. It won’t work. Costs are escalating because governments are reluctant to send migrants away, instead preferring to pressure Venezuela to accept humanitarian relief. They know the conditions are unsustainable there. Meanwhile, ambiguity about the status of Venezuelan migrants in host countries is forcing many to huddle in border areas where they are creating problems for themselves and others. This prevents them from integrating into national communities and formal labor markets.

The U.S. should be more welcoming, too. The mostly middle-class Venezuelans who have flown to Miami have largely managed to receive asylum, but they represent only a tiny fraction of those trapped in legal limbo in Latin America. The liberal democracies of the Western Hemisphere should agree to share responsibility for the humanitarian casualties of Venezuela’s tyrant. They would all benefit from the contributions of Venezuelans desperate to live and work in freedom and peace.