But he's learned more quickly than the last two presidents - especially Barack Obama - that Mitt Romney got it exactly right in 2012: Russian Federation is America's major geopolitical foe.
Tillerson conceded the two world powers had "sharp differences" that have obstructed cooperation but voiced optimism they could make progress. "The U.S. would have to take the field itself, and risk direct confrontation with the Russians and Iranians-highly unlikely", he said.
First came last week's USA strike in response to Bashar al-Assad's deadly sarin-gas attack on innocent civilians.
As Tillerson sat down for talks with his Russian counterpart Sergei Lavrov on Wednesday, a senior Russian official assailed the "primitiveness and loutishness" of USA rhetoric, part of a volley of statements that appeared timed to maximise the awkwardness during the first visit to Moscow by a member of Trump's cabinet.
"Our view is that the reign of the Assad family is coming to an end, and they have again, brought this on themselves", Tillerson said.
Lavrov, meanwhile, said that "the future of Syria has to be determined by the Syrians themselves", echoing a statement Tillerson himself made only days before the chemical attack. And he suggested that possible war crimes charges could be levied against the Syrian leader.
Tillerson reiterated the USA position that Assad must eventually relinquish power in Syria but appeared to take a slightly softer line with Russian Federation.
The civil war is separate from the US-led effort against the Islamic State group in the north of the country.
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In 2013, Putin personally awarded Tillerson the Russian Order of Friendship when the two met to negotiate ExxonMobil's $50 billion deal for Russian oil and gas rights.
But he said Moscow and Washington had agreed to continue co-operating to try to find a political solution for Syria. It's unclear whether Putin will grant Tillerson a meeting. The Kremlin had previously declined to confirm Putin would meet Tillerson, reflecting the renewed tensions.
Moscow and Washington have reached an understanding that further United States strikes similar to the one carried out against Syria's Shayrat Air Base "should not occur again", the Russian Foreign Minister Sergey Lavrov has said.
Trump and others have indeed threatened similar action.
Britain's U.N. Ambassador Matthew Rycroft said it was Russia's eighth veto in support of President Bashar Assad's regime and asked: "How could anyone look at the faces of lifeless children" and yet veto this resolution? "We're going to see how that all works out".
Trump had frequently called during the 2016 United States presidential election campaign for warmer ties with Putin, despite criticism from lawmakers in his own Republican Party.
Russian authorities earlier said a meeting with Putin was not on the agenda, but Kremlin spokesman Dmitry Peskov told reporters the Russian leader could meet with Tillerson "if it is decided" that he needs to be briefed on the outcome of the secretary's talks with his Russian counterpart Lavrov.
The meeting comes as early expectations of an easy rapport between the Trump administration and Russian Federation are crashing into reality.
Allegations of collusion between Russian officials and Trump campaign associates also have weakened Trump's ability to sweeten any offer for greater co-operation, such as by easing economic sanctions on Moscow related to its 2014 annexation of Ukraine's Crimea region and support for pro-Russian separatists in eastern Ukraine.