"Within a few hours" of the nuclear deal being implemented and sanctions lifted "1,000 lines of credit were opened by various banks," Rouhani told reporters in Tehran.
"This showed that those who used to say, 'do not believe' were mistaken," he said, stressing the deal would now make it easier for Iranian businesses to operate after years of being frozen out of the international financial system.
International sanctions lifted after Iran complies with nuclear deal
"Today we are in an atmosphere where we can have political, economic and legal interaction with the world to the benefit of our national interests," the president said.
"We believe in our national strength. We believe in our nation's success," he added.
The remarks were a riposte to doubters who say that the diplomatic success of the nuclear deal will not translate into concrete economic benefits for Iran's economy.
Nuclear deal 'new chapter' in Iran's relations with world: Rouhani
Rouhani staked his presidency on the nuclear talks, deepening the diplomacy which involved Britain, China, France, Russia and the United States plus Germany after taking office in August 2013.
Only last week he said Iranians should look forward to a "year of prosperity" after sanctions are lifted.
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