The once-wealthy oil nation is now facing severe shortages of basic goods and hyperinflation. Trump said the situation in Venezuela is a horrible thing that's "been brewing for a long time."
Temporary Protected Status is granted to people from countries ravaged by natural disasters or war and lets them remain in the U.S. until the situation improves back home.
The Trump administration has moved to discontinue that protection for many countries. But when the president was asked Tuesday about TPS for Venezuelans, he said "we're looking at that very seriously."
Two congressional panels have advanced bills granting protections to Venezuelans, which conflicts with Trump's tough-on-immigration stance.
Carlos Vecchio, who serves as ambassador to Washington for Venezuelan opposition leader Juan Guaidó, said at a Miami press conference Tuesday that he is confident that TPS or some other kind of relief for Venezuelans will come soon, either from the administration or from Congress.
The Trump administration was one of the first to recognized Guaidó as the legitimate president of Venezuela, a measure that was adopted later by more than 50 other nations.
Vecchio thanked Trump for accepting the expired passports of Venezuelans living in the United States, and urged Canada, Spain and Latin American countries to do the same.
On Friday, the opposition-controlled National Assembly approved the validity of Venezuelan passports for five years beyond their printed expiration dates. The same day, the State Department announced that the expired passports will be considered valid for visa applications and entry into the United State.
Around 4 million Venezuelans have fled their country in recent years and many of them don't have a valid passport.
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