The feuding also played out at the United Nations, where Russian Federation was expected to veto a Security Council resolution to bolster calls for global inquiries into the chemical attack.
Putin also claimed Syria - its largest ally in the Middle East - had complied with an agreement to dispose of chemical weapons "so far as we know".
Speaking amid a backdrop of US investigations of Russian meddling in last year's presidential election, Lavrov also said Russia confirmed its willingness to dispel problems in relations with the U.S.
Russian Federation has blocked a draft resolution at the United Nations condemning last week's toxic gas attack in Syria.
Russian President Vladimir Putin meanwhile said trust had eroded between the two countries since Donald Trump became president, after the new U.S. leader fired missiles at Syria to punish Moscow's ally for its suspected use of poison gas. Moscow hasn't seen "a single fact, or even a hint at facts" confirming that the Russians interfered, he said. "Petersburg-bombing-a-notable-absence-Russian-anti-Islam-backlash-video" class="local_link" target="_blank">very large mainly Sunni Muslim community; and in the mainly Muslim Soviet successor states of central Asia, where dictatorship and poverty have created fertile ground for Islamist extremism.
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.
Russian President Vladimir Putin is considering reopening a vital battlefield communications node between his forces and USA troops in Syria, which had been shuttered since Washington's strike on Syrian forces last week. "The world's two foremost nuclear powers can not have this kind of relationship", he said.
It was not clear until the last minute whether Putin would grant Tillerson an audience, but the fact that he did is likely to be seen as a sign that Moscow has not given up on the new US administration and wants to try to improve ties which both sides agree are languishing at a post Cold War low.
The meetings Wednesday "represent a continuation of our communications and discussions and dialogue that began in Bonn", Tillerson said, referring to a G-20 summit on February 16. when he met with Lavrov.
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Kremlin spokesman Dmitry Peskov told reporters on Wednesday that "if it is decided" that the Russian president needs to be briefed on the outcome of the Tillerson-Lavrov talks, he will meet them.
But Lavrov said some progress had been made on Syria at the meeting and that a working group would be set up to examine the poor state of US-Russia ties.
"U.S. and Russian interests, whether in Syria, toward North Atlantic Treaty Organisation, human rights, etc. are far too different-despite President Trump's earlier interest in an understanding".
More than 80 people were killed in what the USA has described as a nerve gas attack that Syrian president Bashar Assad's forces undoubtedly carried out.
He did play down suggestions from some United States officials that Russian forces could have been complicit in last week's slaughter of 87 civilians in the town of Khan Sheikhun.
Trump responded to the gas attack by firing 59 cruise missiles at a Syrian air base on Friday.
The proposed measure - drafted by France, the United Kingdom and the United States, the Council's other permanent members - would have strongly condemned "the reported use of chemical weapons in the [Syria], in particular the attack on Khan Shaykhun", the site of last week's incident that has drawn increasing global attention.
And he declared that numerous divisions between Moscow and Washington were the result of "timebombs" left behind by former president Barack Obama's administration. "We are very unsure about Trump". "And we seek to do that", the veteran diplomat said.
Tillerson, however, used his opening remarks to portray a more diplomatic tone in which he called the talks "an important moment in the United States' relationship with Russian Federation".
"Where is the proof that Syrian troops used chemical weapons?"
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