Trump's right-wing base has long been obsessed by the Epstein saga and conspiracy theories that the financier oversaw a sex trafficking ring for the world's elite.
Formerly Maduro's vice president, Rodriguez, 56, has quickly moved in less than four weeks in power to overhaul Venezuelan society in ways sought by the United States, earning high praise from US President Donald Trump.
Petro leaves office later this year, but for Colombia, the stakes are huge: hundreds of millions of dollars a year in military and other aid and the country's most important trading relationship.
The reopening of Rafah is expected to allow the entry of the 15-member body, known as the National Committee for the Administration of Gaza, which answers to Trump's "Board of Peace".