The field covers 2,400 square kilometres (926 square miles) and is located in Iran's southwestern province of Khuzestan, Rouhani said in a speech aired on state TV
The global oil market had already factored in Iranian oil exports falling to zero under the Trump administration's economic pressure campaign against Tehran.
The advantage with Iran was the attractive terms offered by the country including 60-day credit, free insurance, and shipping
US West Texas Intermediate crude rose 72 cents to $ 66.27 per barrel while international Brent oil rose 35 cents to $ 74.39 per barrel.
The White House announced it was calling an end to six-month waivers that had exempted several countries from unilateral US sanctions on Iranian oil exports
India, Iran's biggest oil client after China, has almost halved its Iran oil purchase since November
The US has made it clear that any country that continues to do business with Iran will be blocked from accessing the American banking and financial system
The cartel had agreed in Vienna in June to push up production in order to put a cap on soaring prices
India continued with Iranian imports even after Trump announced in May that he was withdrawing from the 2015 nuclear deal
Iran's oil output soared to 3.64 million bpd in June from an average of 2.84 million bpd in 2015