Trump says Syrian President Bashar Assad is "an animal". Moscow insists that an "unbiased" worldwide investigation is needed to establish who carried out the chemical attack in Syria on April 4.
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 USA administration and wants to try to improve ties which both sides agree are languishing at a post Cold War low. "The world's two foremost nuclear powers can not have this relationship", he said.
Only minutes earlier, his counterpart, Russian foreign minister Sergey Lavrov, had claimed the two countries agreed work together on a probe of the April 4 chemical weapons attack in northern Syria that prompted retaliatory American missile strikes.
But Russia, an ally of Syria, used its powers in the United Nations to block it.
He said USA secretary of state Rex Tillerson is considering the request.
Mr Johnson said: "This afternoon in NY, the worldwide community sought to make clear that any use of chemical weapons by anyone anywhere is unacceptable and that those responsible will face consequences".
And shortly afterwards, Russian Federation vetoed a UN Security Council resolution that would have demanded Syrian cooperation on the investigation.
At least 30 children were killed in the gas attack.
Putin said Wednesday that U.S. -Russia relations have "degraded" since President Trump took office. Lavrov said the meeting between Tillerson and Putin lasted for over two hours. It's unclear whether Putin will grant Tillerson a meeting.
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Lavrov said Moscow and Washington reaffirmed their commitment to fight worldwide terrorism.
Mr Lavrov blasted USA claims that it has "irrefutable evidence" of election interference. "We want to see all the ethnic groups in the country to feel protected, justly represented in all the branches of government".
"Right now, the world is a mess, but I think by the time we finish, I think it's going to be a lot better place to live". "They were there. So we'll find out", he said.
In a White House press conference with North Atlantic Treaty Organisation secretary-general Jens Stoltenberg, Mr Trump defended the decision to bomb a Syrian airfield after a chemical attack on civilians, stating Russian Federation "could have known" about the attack and chose not to stop it.
Tillerson didn't pin the blame for the attack on Russian Federation, which is involved in the Syrian civil war and supports Assad, but insisted that evidence showed it was carried out by the Assad regime.
Mr Tillerson reiterated the United States view that President Assad should go.
"This one [the Russian veto] is even more regrettable given that Russia was the architect of the 2013 agreement to dismantle Syria's chemical weapons program, an initiative that has demonstrably failed", Rycroft said.
But such hopes appeared optimistic as the diplomats outlined their sharply diverging views on Syria. "We may be at an all-time low in terms of a relationship with Russian Federation", said Trump.