President Donald Trump declared that US-Russia ties "may be at an all-time low", and Mr Tillerson struck a similar tone after a day of talks in Moscow.
Russian Federation had suspended that effort after USA missile strikes on a Syrian airbase following an April 4 chemical weapons attack on a village in rebel territory.
Putin has angrily rejected the accusations against Damascus and slammed the United States bombing as "a violation of worldwide law".
The President and Mr. Mattis appeared eager to underscore that they had no desire to get more involved in Syria amid conflicting signals from within the administration on the future course of action.
Relations between the two powers have become strained over the Syrian crisis amid Moscow's continued support for President Bashar al Assad's regime.
"Frankly, Putin is backing a person that is truly an evil person", Trump said.
However, the Russian President and his officials dismissed United States evidence that Assad had carried out the attack, and Putin added a "bombshell prediction" of his own: Unnamed forces were going to carry out more chemical weapons attacks and blame these on Assad.
Before Rex Tillerson even met Vladmir Putin, harsh words were said against the US.
That leaves substantial open ground between the two countries, compounded by accusations of Russian interference in the U.S. election and disagreements over Ukraine. Russia wants the U.S. to eliminate sanctions on Moscow related to its 2014 annexation of Ukraine's Crimea region and support for pro-Russian separatists in eastern Ukraine.
Mr Tillerson was greeted frostily in the Russian capital as Mr Lavrov began their meeting on Wednesday by demanding to know America's "real intentions". But he said Wednesday the US doesn't have "firm information" to show that Russian forces were involved in the gas attack.
Lavrov said Moscow was hoping to understand Washington's "real intentions" and warned that Moscow considered it "fundamentally important" to prevent more "unlawful" United States strikes against its ally Syria.
Russian Federation said the USA strike was illegal though and Lavrov repeated Moscow's stance on Wednesday, saying an global investigation should be left to determine who was to blame and what happened.
Tillerson's meeting with Putin comes after an icy reception upon arriving in Moscow and a closed-door meeting with Lavrov.
Mr Tillerson repeated the USA administration's belief that "the reign of the Assad family is coming to an end". "And I think it's very bad for Russian Federation", he said in and interview with Maria Bartiromo airing today on Fox Business Network. "We'll see. We'll see the end result, which will be in a long period of time perhaps, but the end result is what's most important, not just talk, and I think that based on everything I'm hearing, things went pretty well".
His administration is now under a congressional investigation over alleged ties with Russian Federation.
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