Ms Haley said that the decision to launch the missile strikes had been to tell Syrian president Bashar al-Assad that "enough is enough" and to let Russian Federation know that is was no longer acceptable to "cover for the regime" anymore.
McMaster says Russian Federation will have to decide whether it wanted to continue backing a "murderous regime" as Trump weighed next steps after ordering airstrikes last week.
But United Nations Ambassador Nikki Haley said there can be no peace in Syria with Assad in power.
Speaking on Fox News Sunday, McMaster said the United States would take further action in Syria if necessary.
Sen. John McCain on Sunday lobbed part of the blame for Syria having used chemical weapons against its own citizens at President Trump and his administration.
Members of Trump's administration have hinted that the U.S.is not done intervening in Syria.
.Russian President Vladimir Putin and his Iranian counterpart, Hassan Rouhani, called for an objective, unbiased investigation into the chemical weapon incident in the Syrian province of Idlib earlier this week, the Kremlin said in the statement.
Reluctant to put significant troops on the ground in Syria, the USA for years has struggled to prevent Assad from strengthening his hold on power. Iran has also contributed Shiite militias to back Assad.
Chelsea's Conte plays down significance of United clash
Subs: Anthony Martial (for Lingard, 63) 5, Marouane Fellaini (for Rashford, 75) 5, Timothy Fosu-Mensah (for Mkhitaryan, 90) 5. Other times you have to play one touch, you keep the ball, you turn, one more touch, you lose the ball.
President Donald Trump ordered the missile strike after watching television images of infants suffering from chemical weapons injuries.
Once that threat "has been reduced or eliminated, I think we can turn our attention directly to stabilizing the situation in Syria", he said.
Haley said "getting Assad out is not the only priority" and that countering Iran's influence in Syria was another.
Russian and Iranian presidents in a phone conversation stressed the inadmissibility of "aggressive" US actions against Syria in violation of worldwide law, the Kremlin said in a statement issued on Sunday.
Assad is known to have previously used chemical weapons against his own people, however, he was supposed to have given up his stockpiles under a 2013 agreement facilitated by Russian Federation.
"We're hopeful that we can prevent a continuation of the civil war and that we can bring the parties to the table to begin the process of political discussions" between the Assad government and various rebel groups, he said.
And the Kremlin said Russian President Vladimir Putin and Iran's leader Hassan Rouhani condemned the cruise-missile attack Thursday on Syria's Shayrat airfield and urged the United Nations Security Council to take action against the USA for launching the attack that violated "the sovereignty of an independent country".
The secretary of state is set to travel to Moscow later this week.
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