Tillerson said he wanted "a very open, candid and frank exchange" as the two men try to figure each other out during the first visit to Russia by a senior member of US President Donald Trump's administration.
"Our meeting today comes at an important moment in our relationship so that we can further clarify areas of common objectives, areas of common interest -- even where our tactical approaches may be different -- and further clarify areas of sharp difference so that we can better understand why these differences exist," Tillerson said.
"Your visit is very timely," Lavrov said, adding it offers an opportunity to clarify the chances of cooperation between the two sides "above all on the formation of a broad anti-terrorist front".
Despite hopes of an improvement in Russia-US ties under Trump, the Tillerson-Lavrov talks look set to be dominated by the war of words over Syria -- where more than 320,000 people have died in six years of war.
But with US officials suggesting Russian forces may have colluded in the latest atrocity blamed on President Bashar al-Assad's regime, it is not clear whether Tillerson will be invited to meet President Vladimir Putin, with the Kremlin only saying there was a "probability" they could talk.
Putin accused Assad's opponents of planning to stage chemical attacks to be blamed on the Assad regime in order to lure the United States, which bombarded a Syrian air base last week, deeper into the conflict.
The Kremlin leader also again slammed the US missile strike and angrily rejected accusations that Assad's forces were behind the suspected chemical attack last week on the town of Khan Sheikhun that left 87 civilians dead including children.
"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," Putin told Mir television.
Trump's spokesman Sean Spicer said Tillerson would go into the meeting with Lavrov to "make sure we let Russia know that they need to live up to the obligations it has made" to halt Assad's chemical weapons use.
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