On Fox News, Haley also said the United States would not pull its troops out of Syria before three goals have been accomplished: defeating ISIL militants, ensuring chemical weapons will not be used and maintaining the ability to watch Iran.
The bombings marked the biggest intervention by Western countries against Assad and ally Russian Federation.
In a televised interview Sunday night, French President Emmanuel Macron said the U.S., France and Britain had "full global legitimacy to intervene" because they had gotten evidence the Syrian government used chemical weapons against its own people and the airstrikes were enforcing worldwide humanitarian law.
Meanwhile, the United States, France and Britain have launched a new bid at the United Nations to investigate chemical weapons attacks in Syria.
According to the lawmaker, Russian Federation is ready for a new round of sanctions, although there is nothing good in this situation. "We're matching", he said. The US ambassador in Moscow, John Huntsman, said in a video, "Before we took action, the United States communicated with" Russia to 'reduce the danger of any Russian or civilian casualties'.
Earlier on Saturday, Syrian police units entered the town of Douma, a site of a suspected chemical weapons attack and the last rebel town in the eastern Ghouta region.
Russian military police had been deployed in Douma, raising complaints from the Syrian opposition that evidence of chemical weapons use might no longer be found. His comments at the closed-door meeting were obtained by Reuters.
Haley said the three US goals for accomplishing its mission are making sure chemical weapons are not used in a way that could harm USA national interests, defeating the Islamic State group and having a good vantage point to watch what Iran is doing. In a US military action a year ago in response to a sarin gas attack, the Pentagon said missiles took out almost 20 percent of the Syrian air force.
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Russian and Iranian military help over the past three years has allowed Assad to crush the rebel threat to topple him.
Britain argued that the strikes were "both right and legal" to alleviate humanitarian suffering from repeated use of toxic gas in attacks in Syria's seven-year war.
The leader of Lebanon's Hezbollah said Sunday that Western strikes on Syria had failed to achieve anything, including terrorizing the army, helping insurgents or serving the interests of Israel.
'We're not going to leave until we know we've accomplished those things, ' she said.
France, the United States and Britain circulated a draft resolution to the U.N. Security Council late Saturday that aims to establish an independent inquiry into who is responsible for chemical weapons attacks in Syria.
Russian Federation and Syria also clashed with the three Western allies over the legality of the airstrikes and responsibility for the Security Council's paralysis. The mechanism would look at cases where the OPCW fact-finding mission has established chemical weapons were used or likely used.
He said, "Ten days ago, President Trump wanted to withdraw from Syria".