But Trump made clear in a landmark speech on Sunday that comity with Iran was not on the table - branding the Islamic Republic the region's major backer of terrorism, and calling it responsible for instability across the Middle East.
"Once again, by his repetitive and baseless claims about Iran, the American president... tried to encourage the countries of the [Middle East] region to purchase more arms by spreading Iranophobia", Iranian Foreign Ministry spokesman Bahram Qassemi said a day after Trump sealed a massive arms deal with Iran's arch-rival, Saudi Arabia, worth $110 billion.
Within hours of Trump's speech Rouhani's rivals were hitting at him hard, calling him responsible for Trump's attack, as well as for the diplomatic success of Saudi Arabia - Iran's regional archrival - in apparently uniting numerous Islamic nations against the Republic.
He fronted two years of hard negotiations with the six major powers that led to a landmark nuclear deal in July 2015.
Mr Rouhani stressed that it was Syrians, Iraqis, Iranians and members of Lebanon's Hezbollah movement who had been fighting terrorists in the Middle East in recent years, and accused the USA and its allies of funding terrorists.
Iran plays a crucial role in fighting terrorism and ensuring regional security and stability and it will continue the same under the 12th government. Americans do not know our region and the problem is that those who are advising the Americans are unfortunately either rulers who are misguiding the U.S., or buying people in the US. It was the Syrians and Iraqis who fought the terrorists and Iran, Hezbollah and Russian Federation were by them.
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The city of Marawi was still largely sealed off Thursday, although automatic gunfire and explosions could be heard. Thirteen militants and seven security personnel have so far been killed and 33 troops wounded, the army said.
"For decades, Iran has fueled the fires of sectarian conflict and terror".
In his news conference, Rouhani vowed to defeat terrorism in the region during his four-year term. The missile launches have been condemned by the Trump administration and Israel.
Incumbent President Hassan Rouhani won a landslide victory in the elections by garnering over 23.4 million of votes (57%) from more than 41 million ballots cast on May 19.
"Our missiles are for our defense and for peace, they are not offensive".
Rouhani conveyed the message that as in recent years Iran has supported the Syrian and Iraqi governments through diplomatic efforts and military advisors, it will maintain this policy in the future.
Trump has said the nuclear accord that world powers reached with Iran is one of the worst deals he's seen and is reviewing policy toward the country. "It would be nice if countries of the region, which give billions of dollars in exchange for America's mirage of support, would give their people the right to self-determination, thus ensuring their stability and well-being", said Qasemi. "We don't need their permission".