Follow along here for the latest updates on the Tillerson-Lavrov news conference.
He said, however, that relations between the two countries are strained and could be improved.
He said there was a "low level of trust" between the nations and "the world's two foremost nuclear powers can not have this kind of relationship".
China, which has vetoed six resolutions on Syria since the civil war began six years ago, abstained from Wednesday's vote, along with Ethiopia and Kazakhstan.
Russian Federation has staunchly backed Assad's government throughout a civil war that has dragged into a seventh year.
Putin also said on Russian TV that the level of trust has "deteriorated".
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In the latest veto, Russian Federation blocked a draft resolution backed by the United States, France and Britain to denounce the attack in the town of Khan Sheikhoun and tell Assad's government to provide access for investigators and information such as flight plans.
Russia's Safronkov called the US strikes on a Syrian air base in retaliation for the Khan Sheikhoun a provocation, but Delattre said they were "a legitimate response to a mass crime which could not go unpunished". "This is contrary to any standards of justice", said Vladimir Safronkov, Russia's deputy envoy to the UN.
The UN motion also would have forced the Syrian Assad government to cooperate in an global investigation into the incident.
"We cannot give up and we must try, in good faith, the best we can, to have a text condemning the attack, asking for a thorough investigation", French Ambassador Francois Delattre told reporters. The same day, Russian Federation pushed back against USA claims regarding the chemical weapons attack.
"I know that there are numerous culprits of people who want to subvert our relations... that is not the issue". "That's exactly what is happening now..." "We'll see what happens".
Until the chemical attack, the Trump administration had sought to step back from the U.S. position that Assad should leave power. "I think he had a very successful meeting in Russia", Trump said. In an interview yesterday, Putin said that if Donald Trump had meant to bring about a thaw in USA relations with Russian Federation, he has failed to see this intention through.