Trump met Venezuela's interim President Delcy Rodríguez at the UN General Assembly, their first face-to-face talks since a US raid seized Nicolás Maduro.
A US-led company gets 100-year concessions over 17 Venezuelan oilfields holding 65 billion barrels, under a deal Trump calls the biggest in oil history.
A Barbados-registered company headed by the Venezuelan businessman Alejandro Betancourt López will run 17 Venezuelan oil fields containing about 65bn barrels of crude.