Haley and Tillerson agreed the fate of ISIS was more important than that of Syrian dictator Bashar al-Assad.
Iranian President Hassan Rouhani said that an worldwide fact-finding committee should be formed to investigate the issue of chemical weapon usage in Syria.
While reluctant to put significant troops on the ground in Syria, the U.S. has struggled for years to prevent Mr Assad from strengthening his hold on power.
Russia's Defense Ministry later said that on April 4, the Syrian air force had delivered an airstrike on the eastern outskirts of Khan Shaykhun to destroy militant facilities used to produce chemical bombs.
British Foreign Secretary Boris Johnson has cancelled a visit to Moscow in light of recent developments in Syria, including Tuesday's deadly chemical attack by the Assad regime, a government statement said Saturday.
When Wallace asked what the United States will do if Russia defends its interests in Syria, mentioning Russian Prime Minister Dmitry Medvedev's comments Friday that the US missile strike in Syria put the two countries "on the verge of a military clash", McMaster stood firm on his position that Russia is "part of the problem" and should become "part of the solution".
"The former ExxonMobil chief executive noted that holding such talks would require the participation of Syrian President Bashar al-Assad's regime along with its allies".
Speaking on Fox News Sunday, McMaster said the United States would take further action in Syria if necessary.
However, Prime Minister Theresa May's official spokesman refused to be drawn on whether the United Kingdom would support further USA military action, saying it was a "hypothetical question".
Russian Federation has stood by the Syrian regime following the atrocity, claiming that Assad's military hit a warehouse used by the rebels to store chemical weapons.
"It can be whatever they wanted to be", McMaster said.
The Iranian President said that this aggression constitutes a "blatant violation of the Syrian sovereignty and all the global laws and conventions", the agency said. I think we desperately needed to send a message that, 'You know what?
Russian and Iranian presidents in a phone conversation stressed the inadmissibility of "aggressive" USA actions against Syria in violation of global law, the Kremlin said in a statement issued on Sunday.
But he added that Mr Trump now needs to work with congress to set a future course.
"We're prepared to do more".
Senator Ben Cardin of Maryland, the top Democrat on the foreign relations committee, agreed.
He said that Trump, on the other hand, acted swiftly and decisively to stop Assad from using chemical weapons ever again.
A U.S. defence official also clarified that the strikes conducted by the nation were not meant to damage runways or fully disable the Syria base.