As he embarked on a trip to Moscow following urgent meetings in Italy with top diplomats, Tillerson said it was unclear whether Russia had failed to take seriously its obligation to rid Syria of chemical weapons, or had merely been incompetent. But he said the distinction "doesn't much matter to the dead".
"We cannot let this happen again," the secretary of state said.
"We want to relieve the suffering of the Syrian people. Russia can be a part of that future and play an important role," Tillerson added in remarks to reporters. "Or Russia can maintain its alliance with this group, which we believe is not going to serve Russia's interests longer term."
Tillerson is travelling to Russia several days after a chemical attack in Syria and a US airstrike on a Syrian government base that Moscow today dismissed as "an act of aggression". Moscow is a staunch ally of President Bashar Assad whom the United States blamed for the chemical attack.
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Since the US launched airstrikes against Assad's forces in retaliation for a chemical attack on civilians last week, Trump administration officials have offered mixed messages about whether Washington believes Assad definitely must surrender power, and when. Tillerson said it was clear the US saw no role for Assad in Syria's future, given that he had lost legitimacy.
"That's why we are not presupposing how that occurs," Tillerson added.
He said the ceasefire talks that Russia and Iran have helped broker in the Kazakh capital, Astana, could generate momentum towards broader talks about a political transition, if the Astana talks succeed in creating a durable ceasefire. The resulting political talks would take place under the auspices of the United Nations process in Geneva.
Tillerson spoke after a meeting of the "like-minded" countries was hastily arranged on the sidelines of the summit of the Group of Seven industrialised economies in Italy, days after the US for the first time launched airstrikes against Assad's forces.
A key focus since the chemical attack has been on increasing pressure on Russia, Assad's strongest ally, which has used its own military to keep Assad in power. The US and others have said that Russia bears responsibility for the deaths of civilians at the hands of Assad given Moscow's role in guaranteeing the 2013 deal in which Assad was supposed to have given up his chemical weapons arsenal.
That accusation will hang over Tillerson's visit to Moscow, where he plans to meet with Russia's foreign minister, Sergey Lavrov, and possibly with Russian President Vladimir Putin. The Kremlin declined to say whether Putin would meet with Tillerson, in line with its usual practice of not announcing such meetings ahead of time.
Though intended to punish Assad for a chemical weapons attack, the US strikes last week served to refocus the world's attention on the bloody war in Syria, now in its seventh year. Diplomats gathered in Italy as US officials in Washington floated the possibility of new sanctions on the Syrian and Russian military, plus the threat of additional US military action if Assad's government continues attacking civilians.
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