Wright arrived in Venezuela on Wednesday. In addition to Rodríguez, he will meet with a number of oil industry executives.
Wright is the highest-ranking representative from Washington to visit Venezuela since the US attack on January 3 that overthrew President Nicolás Maduro.
Venezuela has extensive oil reserves but, according to the oil cartel OPEC, accounts for less than 1 percent of global supply due to poor maintenance and sanctions, among other things.
The US eased sanctions against the country in January after a law was passed in Venezuela allowing private investment in the oil sector.
US President Donald Trump wants major American oil companies to rebuild the sector and increase production by several million barrels a day.
