"America's decision that Iran's oil exports must reach zero is a wrong and mistaken decision, and we won't let this decision be executed and operational," the president said.
Rouhani's remarks come days after a US decision not to renew waivers for Iran's main oil importers.
"In future months, the Americans themselves will see that we will continue our oil exports."
The US had allowed five nations: China, India, Japan, Turkey and South Korea to continue importing Iranian oil despite Washington imposing sanctions on Iran last November. The waivers are set to expire on 2 May.
"This decision is intended to bring Iran's oil exports to zero, denying the regime its principal source of revenue," the White House said in a statement on 21 April.
Saudi Arabia's Energy Minister, Khalid Al-Falih, told RIA news agency that his country would be on hand to plug any gap left by Iran on the global market.
He added that Saudi Arabia would not voluntarily exceed output levels but would meet consumer demand.
"The only indicator I have is consumers' demand for Saudi oil … These figures are moderate at the moment, the demand is healthy, there is nothing to worry about… There is no shortage on the [global oil] market," Al-Falih said.