The letter was partly prompted by an AP investigation, which it cites, that found corruption in Venezuela's food imports.
It also calls for a thorough probe into alleged drug trafficking and support for Middle Eastern terror groups by the country's new vice president, Tareck El Aissami.
El Aissami has been the target of US law enforcement since his days as interior minister almost a decade ago, and has been tied to bribes paid to officials by the nation's top convicted drug trafficker. He has denied any wrongdoing.
And at Congress' insistence, President Barack Obama sanctioned several top Venezuelan officials for cracking down on opponents or helping smuggle cocaine to the US.
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But Trump mentioned the country only briefly during the campaign. And Secretary of State Rex Tillerson's comments during his confirmation gave little sign of whether he will depart from the Obama administration's relative restraint and call for dialogue between socialist President Nicolas Maduro and his opponents.
Venezuela is mired in political gridlock, even as its economy is falling apart. Amid such uncertainty, Maduro has taken a softer tack.
"He won't be worse than Obama, that's the only thing I dare to say," Maduro said last month in an appeal to supporters to withhold judgment on the new US leader.
The letter, co-written by Rep. Ileana Ros-Lehtinen, R-Florida, chair of the house Committee on Foreign Affairs, and Senator Robert Menendez, D-New Jersey, the ranking member of the Foreign Relations Committee, appears intended to force the administration's hand.