"We know there's not any sort of option where a political solution is going to happen with Assad at the head of the regime", she said. Still, Haley said the US didn't see a peaceful future for Syria with Assad in power.
The Syrian opposition has reported that Assad's forces have begun flying again from an air base struck last week by US missiles.
Speaking on Fox News Sunday, McMaster said the United States would take further action in Syria if necessary.
Russian President Vladimir Putin says relations between Moscow and Washington have deteriorated in the early months of Donald Trump's presidency.
"The recent US military attack on Syria is an action of warning", the report said, according to the Associated Press.
Once the threat from IS has been reduced or eliminated, "I think we can turn our attention directly to stabilising the situation in Syria", Mr Tillerson said.
"Three months ago Syria wasn't really an issue for them but our push and recent events have made a difference".
Rouhani also called for an investigation of the suspected chemical weapons attack in Syria last week, and he warned that the U.S. strikes in response risked escalating extremism in the region. Activist Alaa Al-Youssef said that the strike which killed a woman hit a residential neighbourhood.
Defeating the Islamic State group remains the top focus, Tillerson said. He emphasized that point on CBS' Face the Nation, noting that the administration is "hopeful ... we can navigate a political outcome in which the Syrian people, in fact, will determine Bashar al-Assad's fate and his legitimacy".
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On Saturday British Foreign Secretary Boris Johnson announced he had canceled a planned trip to Russian Federation because of fast-changing developments in Syria.
Ms Haley's comments came as Mr Tillerson said he saw no reason for Russian Federation to retaliate over United States missile strikes on a Syrian air base last week.
Dozens of representatives of the media, local authorities, and emergency services have visited the airfield since the attack, with no alleged "storage units" or chemical weapon shells being found, the ministry said in a statement, calling on a mission of professional experts to be sent to the air base.
He said: "Using a deadly nerve agent, Assad choked out the lives of helpless men, women and children". Damascus denies carrying out the chemical attack that provoked the USA response.
Prime Minister Malcolm Turnbull said the Assad regime must be brought into line after last week's chemical gas attack.
The strikes resulted in the death of a woman, and three other people were reportedly wounded in Saturday's attack, two activists in Khan Sheikhoun said.
As the ground rapidly shifted regarding the US approach to Syria, Tillerson made it clear that Washington hopes Assad will not be part of Syria's future.
In the past, Russian Federation and Iran have labeled Assad's opponents as "terrorists".