"I discussed these plans in detail with Secretary Tillerson", Johnson said, adding that the United States foreign minister would still visit Moscow as planned following the G7 meeting to "deliver that clear and co-ordinated message to the Russians".
Iran, which has provided crucial military and political support to Assad, meanwhile called for a fact-finding mission to determine what caused the chemical attack in Khan Sheikhoun.
He, however, backed calls for an independent inquiry into a suspected chemical weapons attack on a rebel-held town in northwestern Syria on Tuesday.
In other developments, a Lebanese official close to the Syrian government said almost 12,000 people will be moved around Syria Wednesday in a planned population transfer arranged between the regime and rebels.
Trump's decision to launch the strikes - which President Barack Obama did not do after a 2013 chemical attack - has raised optimism among USA -backed rebels in Syria that Trump will more directly confront Assad. "So, yes, I'm skeptical", she said.
Saturday's phone call was the first between the top diplomats of Russian Federation and the U.S. since the strikes on the Syrian airfield.
"It's very hard to understand how a political solution could result from the continuation of the Assad regime", McMaster said. Both countries belong to the US -led coalition fighting ISIL militants in Syria.
Iran and Russian Federation are the closest allies of Syrian President Bashar Assad.
Talks Continue as Republicans Face Questions on Obamacare
John Kasich, a Republican, is also getting in on the health care talks. But we can be sure that whatever happens, it's going to be close.
The officials, who insisted on anonymity in order to discuss the sensitive matter, said they believe the hospital attack may have been an effort to cover up evidence of the earlier assault.
Trump's decision to strike Syria won widespread praise from other nations. "Vladimir Putin and [Hassan] Rouhani spoke in favor of an objective, unbiased investigation of all the circumstances of the chemical weapons incident on April 4 in the Syrian province of Idlib".
In a speech on Sunday, Rouhani also criticised USA -allied Gulf Arab states for endorsing the US missile strike.
"What the Americans did is a strategic mistake and offense". U.S. officials noted that the timing of the strike had the possible added benefit of signalling to China that Trump is willing to make good on his threat to act alone to stop North Korea's nuclear pursuits if Beijing doesn't exert more pressure on Pyongyang.
"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.
Russia's Defence Ministry notified the Pentagon it would close down later on Friday the communications line used to avoid accidental clashes in Syria, Interfax new agency said.
The chemical attack killed at least 70 people and injured hundreds others.
"Do they want it to be a relationship of competition and potential conflict?" he continued.