Rouhani rejected meeting with Trump
He claimed the request was raised one day after Trump's speech at the UN, adding that French President Emanuel Macron also tried to persuade Rouhani to accept the meeting with Trump, but was unsuccessful.
Iranian Foreign Ministry Spokesman Bahram Qassemi also confirmed Faza'eli's comments, saying that "this willingness (to meet President Rouhani) was expressed by the American side, but was rejected by the Islamic Republic of Iran's president."
Washington has not yet responded to the Iranian claims, which come weeks after Trump said he would not recertify Iran's compliance with the 2015 nuclear deal.
The president also made clear that the complete cancellation of the 2015 deal is a "real possibility."
Iranian leaders have stepped up their rhetoric in recent days and weeks as it became clearer that Trump was planning not to recertify the deal.
Iran's Foreign Minister, Mohammad Javad Zarif, warned Trump of a "reciprocal measure" if sanctions were reimposed on his country.
Rouhani also criticized Trump's speech and vowed to expand Iran's ballistic missile program.
Iran's Supreme Leader, Ayatollah Ali Khamenei, two weeks ago referred to Trump as “brute” and “stupid”, and also said Tehran would “shred” the nuclear deal if the U.S. withdraws.