Wednesday's meeting brought no indication that the relationship would improve any time soon.
"There is a low level of trust between our two countries", Mr. Tillerson understated during the press conference.
"We responded, along with friend and allies, in a way that made it clear that Russian Federation was extremely isolated on this issue and on the issue of Syria broadly and the behavior of the Assad regime".
The only concession that Tillerson appeared to have extracted from the Russians was that Putin offered to restore a hotline aimed at avoiding accidents in the air over Syria. Until the chemical attack, the Trump administration had sought to step back from the USA position that Assad should leave power.
Hopes may never have been high, especially after Russian Federation sounded a defiant note before Tillerson arrived in Moscow. Tillerson called for Assad to eventually relinquish power.
"Russia is not seeking to cover up for anyone in the chemical weapon incident", he added.
He said "it would be a fantastic thing" if the two nations got along better but cautioned that "it may be just the opposite". The most important part of this was that the United States was not getting in the way.
Only minutes earlier, his counterpart, Russian foreign minister Sergey Lavrov, had claimed the two countries agreed work together on a probe of the April 4 chemical weapons attack in northern Syria that prompted retaliatory American missile strikes.
In the U.S., Trump sought to tamp down speculation he'll intervene militarily against Assad, who is being backed by Russian forces.
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Disagreement over Assad's role in the chemical attack remained an area of tension during the press conference.
The US now assesses that Syria has re-established a unit of personnel associated with chemical weapons that existed before the 2013 agreement in which the Syrian government pledged to give up its weapons inventory.
All-time low, you say?
Lavrov had a ready retort: "This is obviously the subject where our views differ". Ten nations, including the United States, voted in favor of the measure.
This is the eighth time during Syria's six year civil war that Moscow has used its veto power on the Security Council to shield Assad's government.
Mr. Putin has routinely met visiting U.S. secretaries of state since first coming to the presidency in 2000, so not meeting Mr. Tillerson (whose appointment was briefly opposed by U.S. Democrats and Republicans who anxious the former Exxon Mobil chief executive had too many ties to Russia) would have been a significant diplomatic snub.
Later on Wednesday, the Syrian army said that an airstrike by the USA -led coalition killed "hundreds" in Deir al-Zor province when it hit poison gas supplies belonging to ISIS, releasing a toxic substance.
Tillerson reiterated that Assad was behind the attack. "Russian Federation is open to dialogues with the U.S.in different areas, and not only to dialogues but also to joint actions", he said. He mocked NATO's military incursion in Kosovo in 1999. They became well known for their objection to the Iraq War in 2003, when they cast doubt about the presence of weapons of mass destruction in Iraq.
Trump repeated his call for other member states to contribute more funding to the alliance, saying European states "must pay what they owe".