Rouhani gave a televised speech a day after his American counterpart Donald Trump told reporters at a G7 meeting in France that he would be willing to meet with the Iranian leader if the circumstances were right, reports Efe news.
"We're not simply looking to take a photo with someone," Rouhani said.
"A change in our behaviour with those who have put sanctions on the Islamic Republic of Iran and have committed economic terrorism begins with their repentance."
He said the onus was on Washington to revitalize positive progress in its relations with Iran.
The two countries have been at loggerheads since Trump pulled the US out of the historic 2015 Nuclear Deal with Iran last year and re-applied tough sanctions on the Iranian economy.
In response, Iran has scaled back its commitments in the accord.
The remaining signatories of the pact, the UK, France, Germany, China, Russia and Germany, have called for restraint and have petitioned both parties to find a way to open a dialogue.
On the final day of the G7 meeting in Biarritz, southwest France, on Monday, Trump said he was not looking for "leadership change" in Iran and said it could be possible for him to meet with Rouhani in the "coming weeks".
"I think he is going to want to meet and get their situation straightened out," he told a press conference alongside this year's G7 host, France's president, Emmanuel Macron, who has been keen to get Iran deal back on track.
Trump maintains his belief that the 2015 Nuclear Deal was "ridiculous".
The tensions between the US and Iran has increased in recent weeks in the Persian Gulf, especially around the Strait of Hormuz, a narrow corridor separating Iran from the Arabian Peninsula.
A key thoroughfare in the global oil sector, the US has accused Iranian forces of carrying out sabotage against several oil tankers in the region. Both countries have also allegedly shot down each other's unmanned drones.
Tehran also seized a British-flagged tanker of its coast after British authorities seized an Iranian tanker off Gibraltar on suspicion it was shipping oil to Syria in breach of EU sanctions.
( With inputs from IANS )