Addressing his first press conference after being re-elected as Iran's president, Rouhani said that Tehran has always favoured good ties with the regional and worldwide countries.
In a news conference in Tehran on Monday, Rouhani said Trump's first visit overseas was a "theatrical gathering with no practical or political value".
In a jibe at the billion-dollar deals signed between Trump and the Saudi government, Rouhani said: "You can't solve terrorism just by giving your people's money to a superpower".
He was referring to a $110 billion military deal Trump clinched with Saudi Arabia during the US President's first foreign trip since he took office, one of the biggest arms sales in history.
The neologism "Iranophobia" was introduced by a spokesman for the Iranian Foreign Ministry, Bahram Qassemi, who said a day after US President finished his visit to Tehran's regional nemesis, Saudi Arabia, that the US is guilty of "repetitive and baseless claims" about Iran. "I hope it can settle so that we can have a better judgement about those in Washington", said Rouhani.
The 68-year-old leader also said the United States had been wrong in its interventions in Afghanistan, Syria and Yemen.
"The American president tried to encourage the countries of the region to purchase more arms by spreading Iranophobia". 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 USA, or buying people in the US.
Of the 19 hijackers who allegedly carried out terrorist attacks in the United States on September 11, 2001, 15 were Saudi nationals and available evidence suggests some of them were linked to high-ranking Saudi officials.
The US has no other way but to think of "a win-win approach vis-a-vis Iran, otherwise they will fail", he said.
However, speculation has said that Trump may advise Israeli Prime Minister Benjamin Netanyahu to go for closer Israel-Gulf state cooperation as part of an effort to resolve the Israel-Palestine conflict, but also to counter-balance Iranian regional influence.
"Who in the region can claim that without Iran, stability will be maintained in the region?"
He said Friday's election in Iran that saw Rouhani convincingly defeat hardline challenger Ebrahim Raisi had been a message to the world that Tehran was ready for engagement.
He also said Iran would continue with its ballistic missile program.
"Our missiles are for our defence and for peace, they are not offensive. American officials should know that whenever we need to technically test a missile, we will do so and will not wait for their permission", Rouhani said.
Rouhani was a key architect of the 2015 nuclear deal with the USA, the European Union and other partners.
On Monday Trump arrived in Israel, where he again singled out Iran. We are waiting for the new USA administration to find stability and continuity in its policies", Rouhani said."The problem is that the Americans do not know our region and those who advise U.S. officials are misleading them."Rouhani said Iran was the vital force behind the fight against the Islamic State in Iraq and Syria and repeated Iran's official stance that the United States and Saudi Arabia are funding "terrorism" in the Middle East."Who fought against the terrorists?" Many however, interpret both of the aforementioned initiatives, at least in part, as being both out of a shared concern between Israel, the Gulf States and the USA of a rising Iran.
Conservative clerics were also angered by the fact that men and women danced together in the streets of Tehran following Rouhani's election victory, testing the country's strict segregation rules, Reuters reported.