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".
Trump flips on Chinese currency manipulation pledge
CURRENCY: After slumping in the wake of Trump's comments, the dollar steadied at 109.10 yen, compared with Wednesday's 108.80 yen. Trading was also thinner than usual because of the impending Good Friday holiday in the USA and Europe this week, Ng said.
"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.
'Appalling' United Airlines incident won't be tolerated in Canada: Garneau
Dao suffered "a significant concussion as a result of disembarking that plane", Demetrio said in a news conference in Chicago . Demetrio categorized the confrontation as a continuation of bullying tactics used by airlines, particularly United .
"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.
Disclosures Outline The Wealth Of The Trump Administration
White House General Counsel Donald McGahn earned $2.4 million past year as a partner at the Jones Day law firm. Her husband's financial disclosures list the value of her stake at between $5 million and $25 million.