He says the Islamic Republic still is waiting to understand what the Trump administration wants.
Rouhani decisively won a presidential election on Friday, securing another four-year term.
"We know what we are doing", Rouhani told CBS News correspondent Elizabeth Palmer. "We could not protect the system and revolution if it were not for the elections, ballot boxes and the people's presence at ballot boxes", he said in the mausoleum.
"Unfortunately, Americans have always made mistakes in our region", Rouhani said.
Vardan Voskanyan also noted that Iran will continue its involvement in Syria and Lebanon processes and will maintain influential leverages in the Arabian Peninsula and Yemen, continuing to ensure serious presence in Afghanistan developments.
Speaking after Trump's two-day visit to Riyadh, Rouhani said, "This summit was a show and had no political value".
Ultimate power in Iran rests not with the president but with the supreme leader, who is chosen by a clerical panel and has the final say over all matters of state.
A White House official said the deal will help increase Saudi Arabia's defense capabilities, bolstering equipment and services in the face of extremist terrorist groups and Iran. "They should have polling stations in place for the people and let the rulers not be on a hereditary basis". "I hope that the U.S. administration think about the interests of the American people, regardless of the fact that they are not thinking about the interests of other nations".
Paris, which disagrees with Iran over the crisis in Syria, had one of the toughest approaches during the negotiation process between Iran and other great powers in 2015, but then acted swiftly to restore its commercial ties. "Foreign Policy or simply milking KSA of $480B?", Zarif wrote in a Twitter post, referring to the Kingdom of Saudi Arabia.
He made veiled criticisms at security agencies that control large swathes of the Iranian economy and have sought to block his efforts to privatise and attract foreign investment.
"Iran must never be allowed to possess a nuclear weapon - never ever - and must cease its deadly funding, training and equipping of terrorists and militias", Trump said in Jerusalem.
Iranian president also highlighted bilateral and trilateral cooperation along with Russian Federation in regional issues including Astana talks and deemed them a step toward peace and stability in region.
Mr Rouhani also said Iran would continue its ballistic missile programme, which has been heavily criticised by the Trump administration.
"The U.S. leaders should know that whenever we need a missile test because of a technical aspect, we will test", he said.