Tillerson is on a thus-far-futile mission to persuade Putin to abandon support for Syrian President Bashar Assad.
Russian Foreign Minister Sergey Lavrov Wednesday insisted that the US should not carry out further attacks against Bashar al-Assad's regime in Syria.
Both Syria and Russian Federation have denied that forces loyal to the Assad regime carried out the toxic gas attack in the town of Khan Sheikhoun on 4 April.
A senior administration official who briefed reporters Wednesday said it is "very important for us to call out Russian Federation over their sponsorship of the Syrian regime". Tillerson and Lavrov are expected to hold a news conference that begins soon.
Beyond Syria, Russia's alleged meddling in the US presidential election also hovered over what was the first face-to-face encounter between Putin and any Trump administration Cabinet member.
"There is a low level of trust between our two countries", Tillerson said candidly.
U.S. Ambassador to the United Nations, Nikki Haley, called on Moscow to stop protecting Assad and said the United States wants to work with Russian Federation toward a political solution for Syria. The AP also reported that Lavrov said Russian Federation was looking to understand U.S. President Donald Trump's "real intentions". "And actually we strongly believe that there is no contradiction between a strong North Atlantic Treaty Organisation, a credible deterrence and defense and political dialogue with Russian Federation". The diplomats know each other well from Tillerson's days as Exxon Mobil CEO.
It is not the first time Mr Putin and Mr Tillerson have had talks.
Hillary Clinton Discusses President Trump's Airstrikes on Syria
In her first interview since she lost, Clinton said she "wrestles" with the fact that her gender did influence the results. In the first weeks, she largely disappeared from public view, walking in the woods outside her Chappaqua, New York home.
Trump branded the regime leader Bashar al Assad a "butcher" and questioned Russia's role in the chemical attack.
While there was a "low level of trust" between the countries, Mr Tillerson pledged to increase communication between Washington and Moscow.
Russia's deputy United Nations envoy, Vladimir Safronkov, said the draft resolution laid blame prior to an independent investigation.
"We do think it's important that Assad's departure is done in an orderly way", he continued. "We're going to see how that all works out". But in a Fox Business Network interview, the United States president said he wouldn't intervene militarily against Assad unless the Syrian leader resorts to using weapons of mass destruction again.
"We don't want a new Cold War", he said standing next to Trump. "I do not know who saw them".
Lavrov said President Vladimir Putin confirmed his "readiness" to resume a deal on flight safety and preventing incidents with the U.S.in Syria.
Mr Trump has voiced caution on his relationship with Mr Putin, and said he would wait and see about future ties with Moscow.
"I think it's certainly possible".
Putin's view was share by Tillerson who, on the first visit by the Trump cabinet to Russian Federation, said that ties between the two countries were at a low point marked by serious distrust.