Mr Tillerson reiterated the USA position that Syrian President Bashar al-Assad must eventually relinquish power in Syria, a position starkly at odds with Russian Federation.
Mr Tillerson said it was the position of the United States that Mr Assad should go as part of a political solution to the Syrian conflict.
U.S. Ambassador Nikki Haley is warning that the United States will not allow any further use of chemical weapons "to go unanswered". "We are watching the regime's actions carefully".
He said "we may be at an all-time low in terms of our relationship with Russia", but said it would be "a fantastic thing" if the relationship could improve with Russian President Vladimir Putin.
The final draft resolution included a paragraph that the Russians objected to last week stressing Syria's requirement to provide investigators with flight plans and information about air operations on April 4 when Khan Sheikhoun was attacked, names of helicopter squadron commanders, and immediate access to air bases where they believe an attack may have been launched.
The Moscow news conference came after Putin met Tillerson for the first time since Trump took office.
Laying bare deep and risky divisions on Syria and other issues, President Donald Trump declared Wednesday that US relations with Russian Federation "may be at an all-time low".
Syrian President Bashar Assad says a barrage of USA missiles against a military airport after a suspected chemical attack has not diminished his government's ability to carry out strikes.
Tillerson reiterated the USA position that Assad must eventually relinquish power in Syria.
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Mattis sought to explain the strike on Thursday - consisting of 59 cruise missiles launched at a Syrian regime airbase - as a "measured" and "singular" response to the chemical weapons attack - not the beginning of a new war.
Lavrov gave Tillerson an icy welcome, diving straight into Moscow's grievances with Washington in what would usually be warm welcoming remarks.
Russian Federation on Wednesday vetoed a UN Security Council resolution demanding that the Syrian government cooperate with an investigation into the attack.
"This puts Russian Federation on the wrong side of the argument", British Foreign Secretary Boris Johnson said in a statement in London.
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.
A hard task given last week's USA missile strikes on a Syrian air base, in response to what the u-s says was a chemical attack by the Syrian government on its own civilians. He said the two sides would also discuss disagreements on Syria and how to end the country's six-year civil war. He said he knows the two powers have "serious differences", but they also have "common interests and responsibilities".
On North Korea, with Pyongyang reportedly poised to conduct a nuclear test, Trump said he had "great confidence that China will properly deal with North Korea". But he told a news conference at the White House with NATO Secretary General Jens Stoltenberg that alliance members still need to pay their fair share for the European security umbrella. "We're going to see how that all works out", Trump said.
"Right now, we're not getting along with Russian Federation at all".