"I'm a strong supporter that the US should take action to protect humanitarian causes like the ban on use of chemical weapons".
Russian Federation had agreed to "be the guarantor of the destruction of Syria's chemical weapons stockpiles. the result of their failure has led to the killing of more children and innocents", Mr Tillerson added.
Theresa May and Donald Trump have agreed a "window of opportunity now exists" to persuade Russian Federation that its links with Bashar Assad's regime are no longer in its strategic interest as they discussed the situation in Syria.
A week ago, Haley and Tillerson said that the U.S. was not working towards unseating Assad, and that such a decision should be up to the Syrian people.
Both Tillerson and H.R. McMaster, Trump's national security adviser, said defeating the Islamic State group remained the administration's first priority, with the strategy for stabilizing Syria a longer-term political effort that could involve Russian Federation.
Mrs May's official spokesman refused to be drawn on whether the United Kingdom would support further U.S. military action, saying it was a "hypothetical question".
But Secretary Tillerson called Russian Federation "incompetent" for allowing Syria to hold on to chemical weapons in interviews on Sunday, while America's United Nations ambassador Nikki Haley told CNN her country wanted regime change.
In a significant shift from the White House's stance on the Syrian president - just a week ago the Trump administration acknowledged the "political reality" of Assad remaining in power - Ms Haley said that Mr Assad must go.
A United Kingdom government source said: "The important thing is that this is Britain helping to influence U.S. policy on Syria and Russian Federation, far from being a poodle".
But Ms Haley warned that the U.S. was prepared to "do more" if needed, leaving the door open for more military intervention as the global community awaits a response from President Assad and his allies.
"We don't see a peaceful Syria with Assad in there", she said. Washington blamed the Syrian government for the incident, saying chemical weapons used in the alleged attack originated from the airfield.
Pressed to clarify, McMaster said the goals of fighting the Islamic State and ousting Syria's president were somewhat "simultaneous" and that the objective of the missile strike was to send a "strong political message to Assad".
Several lawmakers said Sunday that decision shouldn't entirely be up to Trump.
McMaster spoke on "Fox News Sunday", Tillerson appeared on ABC's "This Week" and CBS' "Face the Nation", and Haley was on NBC's "Meet the Press" and CNN's "State of the Union".
Tillerson, on the other hand, stressed that the air strike had the limited aim of deterring further use of chemical weapons.
Haley said "getting Assad out is not the only priority" and that countering Iran's influence in Syria was another.
"I think the president has authorization to use force", he said.