Speaking live on state television from the central city of Yazd, Rouhani said on Sunday the field was located in the country's southern Khuzestan province, home to its crucial oil industry.
"I am telling the White House that in the days when you sanctioned the sale of Iranian oil, the country's workers and engineers were able to discover 53 billion barrels of oil," he said, according to the semi-official Fars news agency.
Oil reserves refer to crude that is economically feasible to extract. Figures can vary wildly by country due to differing standards, though it remains a yardstick of comparison among oil-producing nations.
Iran currently has the world's fourth-largest proven deposits of crude oil and the world's second-largest deposits of natural gas.
The new oil field could become Iran's second-largest field after one containing 65 billion barrels in Ahvaz.
The field is 2,400 square kilometres (925 square miles), with the deposit some 80 metres (260 feet) deep, according to the semi-official Tasnim news agency.
Manouchehr Takin, international oil consultant, told Al Jazeera that the announcement did not reveal how much oil could be produced from the reservoir.
"The announcement was made by politicians. They haven't given many technical details," he said. "Whether it is 53 billion barrels is oil in place or whether it is recoverable. Even if it is oil in place, I would say about 20 or 30 percent can be recovered, it is a huge quantity.
"Making a discovery is different from producing," he added. "And of course, to produce oil and gas takes time. It depends on the particular characteristics of this reservoir that has been discovered ... I would say at least 2 or 3 years minimum [before production can start]."
The deal imposed curbs on Iran's nuclear programme in exchange for relief from international sanctions.
After withdrawing, the US also reinstated sanctions to choke Iran's oil exports and isolate its economy as part of a "maximum pressure" campaign against Tehran to force it to negotiate a new deal.
In June, Trump signed an executive order imposing new sanctions on Iran's top leadership, including Supreme Leader Ali Hosseini Khamenei, in a move denounced by Iran as "useless" and signalling "the permanent closure of the path of diplomacy".
On Saturday, Iran said that it was enriching uranium to five percent in its latest step away from its commitment under the troubled accord that set a 3.67 percent limit.