Tillerson made his remarks during a joint press conference Saudi Foreign Minister Adel al-Jubeir a few hours after the United States and Saudi Arabia inked an arms deal worth some $100 billion effective immediately, along with another military agreement worth $350 billion over the next 10 years.
"If Rouhani wanted to change Iran's relationship with the rest of the world, those are the things he could do", Tillerson said.
"The two countries signed a series of agreements", Adel al-Jubeir told reporters at a joint press conference with US Secretary of State Rex Tillerson.
Minister Al-Jubeir described the day as a truly historic one for U.S. -Saudi relations, further deepening the ties between the two longstanding allies.
"Additionally it bolsters the Kingdom's ability to provide for its own security and contributing to counter-terrorism operations throughout the region".
The "Ardha" performance was hosted by King Salman on Saturday to mark President Trump's first overseas visit to Riyadh.
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President Donald Trump said the first day of his maiden global trip has been "tremendous".
Mr Trump appears to be taking a tougher stance on Iran compared to his predecessor Barack Obama, pleasing Saudi Arabian officials.
There have also been no direct US-Iranian talks since Trump took office. The White House bungled the president's stunning firing of FBI Director James Comey, who was overseeing a federal investigation into possible ties between Trump's campaign and Russian Federation.
A few days later, the Trump administration imposed sanctions on multiple Iranian entities and individuals after the Islamic Republic defied a United Nations Security Council resolution by launching a ballistic missile test.
Secretary of State Rex Tillerson said he'll talk with his Iranian counterpart "at the right time" after elections in Iran saw moderate President Hassan Rouhani returned to power. As CEO of ExxonMobil, though, Tillerson was involved in negotiations and agreements with Saudi Arabia and other Middle East countries and has a great deal of knowledge about its leaders.