Rouhani also condemned use of chemical weapons in Syria, saying it was "regrettable".
Nikki Haley, the US ambassador to the United Nations, said the departure of Syrian President Bashar Assad is a USA priority, just as it was under the Obama administration, and that peace in Syria was probably impossible while he remained in power.
Until her appointment in January, the former SC governor had never been involved in worldwide politics or foreign relations before.
Both Tillerson and H.R. McMaster, Trump's national security adviser, said defeating Daesh remained the administration's first priority, with the strategy for stabilising Syria a longer-term political effort that could involve Russian Federation.
The White House said Monday that the U.S.is open to further action on Syria if Damascus continues to use chemical weapons.
She's highly critical of Syrian president Bashar al-Assad.
Earlier this year, Assad said that the country's government had never used weapons of mass destruction, including chemical weapons, against the Syrian people.
Rohani called the US strike a "blatant violation" of Syrian sovereignty while dismissing reports that Assad's regime was behind the deadly gas attack as "baseless".
Syria has denied using any chemical agents, and Russian Federation says the USA gave no evidence Syria has chemical weapons.
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They also see Russian Federation as a foreign occupier whose relentless aerial bombardment of rebel-held areas has led to thousands of civilian casualties.
President Trump's long-term intentions in Syria thus remained unclear in the days since 59 Tomahawk missiles tore into a Syrian air base that USA officials said was used to launch a deadly poison gas attack on April 4 that killed about 80 Syrian civilians and injured dozens more.
"And we have to make sure that we're pushing that process". "Or do they want it to be a relationship in which we can find areas of cooperation that are in our mutual interest?" Additionally, she said USA sanctions against Russia would remain until the Russian government and its allies "respect Ukraine's sovereignty and territorial integrity".
Haley has publicly called herself the "proud daughter of Indian immigrants".
Haley was harsher on CNN's "State of the Union".
However, Haley's stance on the refugee crisis has been murky. After she criticized Russian Federation for not caring about dying children, last week the ambassador was heckled by an audience member at a conference because Trump's now-halted executive order on immigration stopped the US refugee program for at least 120 days.
Just days before the chemical attack, Haley and Tillerson both had indicated that removing Assad from power was no longer a U.S. priority.
Shortly after the conference, Haley went on NBC's Meet the Press to explain the discrepancy, which she chalks up to an issue of vetting. "What this president has done is said, 'Prove to me that you are vetting these people properly. We're not going to have you cover for this regime anymore'".
But Haley suggested there has been a shift in United States thinking.