For other matters, Switzerland is the nation that officially represents USA interests in Iran since the US cut off all ties after the 1979 Iranian revolution.
The United States has told third countries they must halt imports of Iranian oil from early November or face USA financial measures. The Iranian rial has fallen to 99,000 to the US dollar despite a government-imposed rate of 44,000.
Rouhani, a pragmatist who was instrumental in Iran's 2015 nuclear deal with the United States, is facing strong headwinds because US President Donald Trump pulled Washington out of that deal in May and has threatened to reimpose sanctions in order to choke its oil-exports driven economy.
Trump said this week he is willing to meet with Iran's leadership, without preconditions, "whenever they want" - a sharp departure from his threats against the regime last week.
Rouhani and his foreign policy team will be in NY in September for the UN General Assembly; both he and Trump will deliver speeches on the same day, Sept. 25.
If the re-imposed sanctions caused the government in Tehran to collapse, Iran would likely devolve into civil war like what unfolded in Syria or radicals would assume power, the diplomat said.
For Iranian leaders to smile and shake Trump's hand would symbolize a deep capitulation and recognition that the United States holds tremendous power over Tehran, and that their values of opposing U.S. hegemony stand subordinate to their will to survive economically, for which they'll need a benevolent Trump.
The U.S. also has banned imports of Iranian products such as carpets and pistachios and revoked licenses that allowed Iran to purchase U.S. and European aircraft.
"The slogans in this protest were against the Islamic Republic of Iran and not about high inflation", the deputy of Fars governor for security, social and political affairs Hadi Pajohezh, told IRNA.
Or the regime could start to address what America calls its "malign influence" in the region, including its support to Syrian President Bashar Assad and threats to shut down the strategic Strait of Hormuz, a vital shipping lane for global oil supplies.
Footage posted online showed dozens of marchers in central Tehran chanting, "Death to the dictator", referring to supreme leader Ayatollah Ali Khamenei. Authorities reported the first fatality among protesters, with the shooting of a man in Karaj, west of Tehran.
But before that, the last time a sitting US president actually met with an Iranian leader was before the revolution when Jimmy Carter met with the Shah of Iran.