H.R. McMaster, the White House national security adviser, arrives at the Pentagon on March 16.
He said he will remind his counterpart of Russia's obligation to act as the guarantor of the agreement to eliminate chemical weapons from Syria.
Saudi Arabia said on Friday it "fully supports" U.S. strikes on military targets in Syria, saying it was a "courageous decision" by President Donald Trump in response to the use of chemical weapons against civilians. "I think the president has authorization to use force".
Syrian warplanes have reportedly taken off from the air base targeted by USA air strikes, less than 24 hours after it was pounded by dozens of Tomahawk missiles.
Russian prime minister Dmitry Medvedev also said that the United States strikes were one step away from clashes with Russia's military.
"Someone who uses barrel bombs and chemicals to kill his own people simply can not be the future leader of Syria", he said of President Bashar al-Assad. "It was a very deliberate, very proportional, and - and very targeted strike undertaken in response to the chemical weapons attack".
Secretary of State Rex Tillerson spoke with Russian Foreign Minister Sergey Lavrov on Saturday about the situation in Syria, a longtime Russian ally. Russian Federation is the Syrian regime's main ally in the nation's six-year-long civil war.
U.S. Ambassador to the U.N. Nikki Haley had a stronger message for Russian Federation last week, saying, "How many children have to die before Russian Federation cares?"
In one of those interviews, Tillerson said he sees no reason for retaliation from Russian Federation for the US missile strikes.
Russian Federation maintains a close political and military alliance with President Assad's government and has been accused of supporting its attacks against Syrians opposed to Assad's rule - something Moscow adamantly denies. "Their initial reaction was, 'Assad didn't do it".
United Nations war crimes investigators have opened a probe into the chemical attack, with UN Syrian envoy Staffan de Mistura saying all indications were that "it was a chemical attack and it came from the air". He suggested on the campaign trail that Assad was an unsavory but stable ruler, and that the US should not focus on pushing him out of power.
U.S. Ambassador to the United Nations and U.N. Security Council president Nikki Haley listens during a U.N. Security Council meeting on Syria, at the U.N. headquarters in NY on April 7.
"It can be whatever they wanted to be", McMaster said. "How was it in anyone's interest that this conflict in Syria and this catastrophe in the greater Middle East continue?"