This is the eighth time that Russian Federation has vetoed a resolution on Syria ever since the nation got embroiled in its long-drawn civil war.
At the news conference after the Putin meeting, Tillerson reiterated the US position that Assad's regime was responsible for the chemical attack.
The press conference came just moments before Russian Federation again cast a veto at the UN Security Council, blocking a bid from the US, UK and France to condemn the suspected gas attack and push the Syrian government to cooperate with investigators.
He restated America's claim that Syrian government forces "planned, directed and executed" a chemical attack on civilians which killed more than 80 people. But Tillerson repeated the administration's new belief that "the reign of the Assad family is coming to an end".
Trump's top aides said earlier this month that the President was moved by the photos and video of children suffering from the effects of the chemical attack and that those pictures, in a way, compelled him to take action against the Syrian president.
"It's deplorable, and we regret what is going on, but we can do little except asking to back accusations with facts", Lavrov said.
Reporters asked whether Tillerson had introduced evidence at Wednesday's meetings of Russian interference in the USA election.
"There is a low level of trust between our two countries".
But such hopes appeared optimistic as the diplomats outlined their sharply diverging views on Syria.
Russian diplomats urged patience and for the United States and others not to rush to judgment over the April 4 chemical weapon attack that killed more than 80. And he suggested that possible war crimes charges could be levied against the Syrian leader.
Both Syria and Russian Federation have denied that forces loyal to the Assad regime carried out the toxic gas attack in the town of Khan Sheikhoun on 4 April. The U.S. intelligence community has concluded Moscow attempted to influence the election in Trump's favor.
While the most immediate U.S.
Tillerson was greeted frostily in the Russian capital as Lavrov began their meeting Wednesday by demanding to know America's "real intentions".
Tillerson said the U.S. is confident in its assessment that Syrian government forces used chemical weapons in the bombing on Khan Sheikhoun and alleged that Syria has used such weapons more than 50 times in the past. "We believe it is of principal importance to prevent risks of a repeat of such steps in the future". "I think it's probably unlikely, and I know they are doing investigations into that right now", said Trump. But in a Fox Business Network interview, the USA president said he wouldn't intervene militarily against Assad unless the Syrian leader resorts to using weapons of mass destruction again.