Iranian President Hassan Rouhani makes a speech during a ceremony in Tehran, Iran on January 10, 2019.Anadolu Agency | Anadolu Agency | Getty ImagesOil slid after Iranian President Hassan Rouhani claimed Friday that the U.S. offered to remove all sanctions on Iran in exchange for negotiations. President Donald Trump and the State Department later denied those claims, causing oil to rebound from the lows.WTI crude futures were last up by 0.1% to $56.46 after falling as low as $54.79. Brent crude futures dropped 0.6% to $62.38.”The German chancellor, the prime minister of England (Britain) and the president of France were in New York and all insisted that this meeting take place. And America says that it will lift the sanctions,” Rouhani said on his official website, according to Reuters. “It was up for debate what sanctions will be lifted and they (the United States) had said clearly that we will lift all sanctions.”Trump later said he responded “of course, NO!” to Iran who he said wanted him to lift the sanctions in order to meet.The State Department called the report “baseless,” adding the U.S. is committed to zero oil exports from the Iranian regime, Bloomberg News said.Rouhani’s comment came after a series of drones attacked oil facilities in Saudi Arabia on Sept. 14, which had forced the kingdom to cut production in half. The U.S. and some European countries, as well as Saudi Arabia, have blamed the attack on Iran. Tehran has denied any role in the incident. The Trump administration also announced plans to deploy U.S. forces to the region.The State Department didn’t immediately respond to CNBC’s request for comment.”There’s been a big bearish risk from a thaw in the US Iran situation for some time and this will put a remarkable amount of oil back onto the market immediately if it were to occur,” said John Kilduff of Again Capital.”It’s not just Iranian production and exports. Its’ millions of barrels in floating storage and millions of barrels sitting in China’s ports waiting to be processed by customs,” Kilduff said.Trump last year withdrew the U.S. from a nuclear deal between Iran, the U.S. and five other countries that removed sanctions from the country in return for its commitment to end its nuclear.The Islamic Republic, a target of U.S. sanctions for decades, was blamed by Washington for recent attacks on oil tankers in the Strait of Hormuz, which Tehran denies. Iran also shot down a U.S. military drone and announced plans to execute 17 suspected U.S. spies.This is a developing story. Check back for updates.— CNBC’s Patti Domm contributed reporting.