Foreign ministers from the Group of Seven major industrialised nations meet on Monday for an annual gathering, with Europe and Japan seeking clarity from the United States on an array of issues, especially Syria.
To be clear, our military action was a direct response to the Assad regime's barbarism.
Before setting off for Moscow, Tillerson told a G7 foreign ministers' meeting in Italy that Russian Federation should rethink its alliance in the light of the latest alleged chemical attack in Syria.
"It's clear that the Russians are trying to cover up the attack", said one of the senior White House officials.
Pressed by reporters on the future of Assad, he added: "In terms of the future of Bashar al-Assad, it is important to us that we undertake a political process that leads to the final conclusion of how Syria will be governed".
The G7 ministers failed to agree on whether fresh sanctions should be imposed on Damascus and Moscow.
The top American diplomat plans to use his meetings with foreign ministers from the Group of 7 industrialized economies - normally a venue for wonky economic discussions - to try to persuade leading countries to support the USA plan.
"So I am dismayed that Russian Federation has once again blocked the UN Security Council and in so doing refused to condemn the use of chemical weapons or support a full UN investigation into the attack".
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In the aftermath of the US cruise missile strike on the Shayrat military facility, Syria rushed to announce that the airbase was up and running within 24 hours.
Putin also claimed, without evidence, that there are plans to fake the use of chemical weapons in Syria. Now there are reports that America believes Russian Federation knew in advance about the alleged Syrian chemical weapons attack that prompted America's missile strikes in the first place.
The strike was the first time Washington had intervened directly against the regime of Assad, who is fighting a six-year civil war with the backing of Russian Federation and Iran.
Mr Tillerson said there was "a low level of trust" between both countries and such a relationship could not be allowed to continue between the world's foremost nuclear powers. The Syrian government has denied it was behind the assault.
Meanwhile, the United States has vowed to keep up the pressure on Syria.
Trump says it's also "very bad for mankind".
But US officials later appeared to go back on Spicer's remarks.
News agencies quoted Italian foreign minister Angelino Alfano as saying the session devoted to Syria was called in an effort to prevent a "dangerous military escalation" in the six-year-old conflict.