"The worldwide community will not allow chemical weapons to come back into our everyday life", she said in an interview aired Sunday.
The airstrikes were carried out in response to an alleged chemical weapons attack in the Syrian town of Douma last week.
"Everyone is going to feel it at this point", Haley said, warning of consequences for Assad's foreign allies. "I think everyone knows that we sent a strong message, and our hope is that they listen to it", she told CBS News on Sunday.
European Union foreign ministers will discuss the air strikes in Luxembourg on Monday, amid concerns by some member states about the legality of the operation without United Nations approval, and about the categorical attribution of responsibility to Syria ahead of reports from the inspectors on the ground.
"We're not going to leave until we know we've accomplished those things", she said.
The Barzeh facility is thought to be the centre of Syria's chemical weapons program, while chairman of the United States joint chiefs of staff, General Joseph Dunford, said Him Shinshar was "the primary location of Syrian sarin and precursor production equipment".
He said the action was "not an attempt to change the tide of the war in Syria or to have regime change". "This was not muscle flexing".
"Stepping up support for Assad so he has cover to keep doing this, being more hostile in Eastern Europe, things like that we might want to be anxious about", he said. "Our job was never to start a war".
That means an end to chemical weapons usage, the complete defeat of ISIS in Syria, and curbing Iranian influence in the area.
Right now there are 2,000 American troops in Syria.
In Istanbul, protesters outside the French Consulate demonstrated against the "imperialist aggression in Syria" while those in Baghdad carried Syrian flags as a show of unity as they burned U.S. flags.
"It looked awfully to me as though the prime minister was more interested in following Donald Trump's lead than anything else", Corbyn said.
Missiles in the skies over Damascus. We hear from him. "President Trump is not a king".
Kaine said the Syrian operations lack a clear strategy. Corbyn said Sunday that he was not convinced the military intervention had been legal under global law. "We need to defeat ISIS".
But, he says direct military conflict with Russian Federation is not likely. "It should be taken as part of a strategy". "This is not about trying to turn the tide of the conflict in Syria", he told the BBC, adding that Russian Federation was the only country able to pressure Assad to negotiate an end to the conflict.
· Syria and its allies, Russian Federation and Iran, have repeatedly called the alleged gas attack in Douma a "fabrication" used to justify military intervention.
"By its actions, the United States is increasingly exacerbating the humanitarian catastrophe in Syria and bringing sufferings to civilians", said President Vladimir Putin.
Speaking to Rouhani by telephone the day after US-led strikes on suspected chemical weapons facilities, Putin said "if such actions, carried out in violation of the United Nations Charter, are repeated, that would inevitably provoke chaos in global relations", according to a statement from the Kremlin.
Mr Cable told Sky News it was a "mistake" to launch the strikes "without getting proper political endorsement", adding the move was a "mistake of judgement" borne out of political weakness.