Secretary of State Rex Tillerson said he had a "productive" and frank two-hour meeting on Wednesday with Russian President Vladimir Putin and his foreign minister, Sergey Lavrov.
Russian Federation vetoed a UN Security Council resolution that would have condemned the use of chemical weapons in Syria last week and called on the government there to cooperate with an investigation into the incident.
"We have seen very alarming actions recently with an unlawful attack against Syria", Lavrov said, referring to the 59 Tomahawk missiles Trump launched at an air base to punish Assad for using chemical weapons.
"Clearly, our view is that the reign of the Assad family is coming to an end", Tillerson said.
Russian Federation says the chemicals that killed civilians last week belonged to rebel forces, not Assad's government, and accused the United States of acting on a false pretext.
Two days after, the United States launched 59 cruise missiles against the Shairat military base in central Syria, where from, according to the USA, airplanes carrying chemical weapons took off. Russia, Assad's staunchest ally, has insisted that Assad is blameless and that it was actually the rebels responsible for the disbursed chemical weapons. Lavrov said a "deconfliction" hotline would be restored to avoid inadvertent collisions by the air forces of both countries in the Syrian war zones.
Western allies say there is compelling evidence that the Syrian government was behind what happened in Khan Sheikhoun.
In Paris, French President Francois Hollande said, "Russia bears a heavy responsibility" by systematically opposing multilateral action to protect its Syrian ally Assad.
The resolution was brought by the so-called P3 - the U.S., U.K., and France.
As a refresher, these words come amid an investigation into the scope of Russia's meddling in the 2016 election and what, if any, connection Trump's campaign staff and transition team may have had with the country as the meddling occurred.
Safronkov also said the USA airstrike on the al-Shayrat air base last week violated global norms.
They had said it was "very clear" sarin or a sarin-like substance was used.
However, the Syrian envoy to the UN Bashar Ja'afari dismissed as "lies" and "accusations" the notion that his country used "a chemical weapon we do not even possess".
Russian Federation has slammed Washington s attack on a Syrian airbase and, as the top diplomats met, Putin admitted that relations between Washington and Moscow have worsened in the three months that Trump has been in office.
Assad himself said the chemical attack was fabricated in an Agence France-Presse interview Thursday.
Despite hopes of an improvement in ties under Trump, the fallout over the alleged chemical attack and USA bombing meant the Syrian conflict - in which more than 320,000 people have died - has dominated Tillerson's visit.
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. The main problem was that the "troika" of drafters had named a perpetrator before a proper investigation had been conducted, he said, adding that by presenting a "doomed" resolution they had undermined the Council's unity.