In the wake of the meeting Russia then vetoed a US-backed resolution at the UN demanding the Syrian government cooperate with an investigation of a suspected chemical attack that the West blames on Moscow's ally Bashar al-Assad.
US president Donald Trump's White House victory had raised hopes in Moscow that some kind of rapprochement was possible between the former Cold War foes.
Trump had spoken warmly of Russia on the campaign trail, but since he came to office in January ties have chilled and the fallout from the alleged chemical weapons attack in Syria threw them into crisis.
Trump envoy Tillerson's talks with Putin and Foreign Minister Sergei Lavrov have been haunted by the incident that saw the US launch punitive strike against Assad's forces.
On the alleged attack, and issues like Russian intervention in Ukraine and alleged interference in the US election, the viewpoints of Moscow and Washington remained far apart.
"We frankly discussed the state of US-Russian relations. I expressed that the current state is at a low point," the US envoy and former oil executive told reporters.
"There is a low level of trust between our two countries. The world's two foremost nuclear powers cannot have this kind of relationship," he warned.
Lavrov had begun the day with the more combative tone, but at the pair's joint news conference it was he who stressed the areas where closer cooperation remains possible.
"Despite the quantity of existing problems... there are considerable prospects for joint work," Lavrov said, after he took Tillerson for private talks with Putin.
"Russia is open to this, open to dialogue with the US in all different areas," he insisted, citing the capitals' shared vision of an "uncompromising" war on terrorism.
And he said that Russia was open to restoring a "deconfliction" hotline to enable US and Russian military commanders to avoid accidental clashes over Syria.
But neither side cited much in the way of concrete new avenues of cooperation, beyond establishing a working group to address what Tillerson called "smaller issues."
The news conference was dominated by points of contention, chiefly Moscow's deep aversion to US interventionism and Washington's disgust at the carnage in Syria and Ukraine.
Tillerson was once a familiar and friendly face in Moscow as the chief executive of oil giant ExxonMobil, but he pulled no punches on his first visit as secretary of state.
He restated the US beliefs that Russian hackers and propagandists interfered in the US vote and that Assad's forces were behind the latest chemical weapons attack.
Missile salvo
He did play down suggestions from some US officials that Russian forces could have been complicit in last week's slaughter of 87 civilians in the town of Khan Sheikhun.
But he was firm that only Assad's forces could have carried out such a strike and insisted that Russia must do more to help strip the regime of its chemical arsenal.
Lavrov parried the accusations, noting that Moscow wants UN weapons investigators to probe not only Khan Sheikhun but also the Syrian air base that US missiles hit in response.
And he declared that many of the divisions between Moscow and Washington were the result of "timebombs" left behind by former president Barack Obama's administration.
"We are realistic and understand the need to overcome these obstacles we have to make efforts. And we seek to do that," the veteran diplomat said.
Putin, in a television interview ahead of the talks, was more blunt about the new chill in ties, and firmly rejected Washington's view of the Syrian attack.
"You can say that the level of trust on a working level, especially on the military side, has not improved but most likely worsened," he said.
"Where is the proof that Syrian troops used chemical weapons? There isn't any. But there was a violation of international law. That is an obvious fact."
Tillerson had said he would challenge Russia to distance itself from Assad and his Iranian backers, an idea that the Kremlin dismissed as "absurd".
Russia vetoes UN resolution
And -- even as Tillerson, Putin and Lavrov discussed their differences in Moscow -- a fresh storm broke at the United Nations Security Council in New York.
Russia vetoed a resolution tabled by the US, Britain and France tabled on the alleged chemical attack in Syria.
It was the eighth time that Russia has used its veto power at the UN Security Council to block action directed at its ally in Damascus.
Putin meanwhile accused Assad's opponents of planning to stage chemical attacks to be blamed on Damascus in order to lure the United States deeper into the conflict.
In a sign the Kremlin is not ready to drop Assad, Syria's foreign minister will jet in to Moscow to meet Lavrov on Thursday before a three-way meeting with Iran on Friday.
Eyewitness? Submit your stories now via social or:
Email: news@pulselive.co.ke
