But Tillerson, who is expected to visit Moscow on Wednesday for talks with Russian officials, said on ABC's This Week program there was "no change" to the USA military posture towards Syria.
"We don't see a peaceful Syria with Assad in there", she said.
The United States is prepared to "do more" if necessary in Syria, US ambassador to the United Nations Nikki Haley said on Sunday.
US Secretary of State Rex Tillerson has criticised Russian Federation, saying it had failed to prevent Syria from carrying out a chemical attack on a rebel-held town. "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.
White House National Security Adviser H.R. McMaster said Syria's "sponsors", Russian Federation and Iran, were enabling President Bashar al-Assad's "campaign of mass murder against his own civilians".
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"I believe that the United States of America can address both at the same time", McCain said.
McCain also said he doesn't agree with Tillerson's stance that the U.S.
During the 2016 presidential campaign, Trump said defeating Islamic State was a higher priority than persuading Assad to step down.
But instead of regime change, what we should focus on is humanitarian relief ...
Graham spoke several days after Trump unilaterally ordered a missile attack on a Syrian airbase in response to Assad's deadly chemical weapons attack on civilians and as the Trump administration tried to explain its foreign policy.
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United States forces have conducted a number of air strikes on jihadist bases in the area since August past year . White House spokesman Sean Spicer said ISIS fighters had used the tunnels and caves in Achin to maneuver freely.
"I think the real failure here has been Russia's failure to live up to its commitments under the chemical weapons agreements that were entered into in 2013", Tillerson said.
Graham may have been blunt, but his sentiment is shared by several of his colleagues and many Americans who are frustrated by the Assad regime's merciless chemical attacks.
"What we are saying is other countries have to ask themselves some hard questions".
"There seem to be a difference in what Ambassador Haley is saying, that Assad has no future, and what I heard this morning from Secretary Tillerson", Republican Senator Marco Rubio told ABC, adding that Tillerson's strategy won't work.
"There is no such thing as Assad yes, but ISIS no", Rubio said.
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