But he renewed his argument that NATO's member states need to dedicate two percent of their gross domestic product to military expenditure.
Meanwhile, President Trump told the Fox Business Channel that Assad was a war criminal and Russian Federation should rethink its support of him.
Our chief foreign affairs correspondent, Margaret Warner, has our report.
Tillerson and his Russian counterpart, Foreign Minister Sergey Lavrov, are also meeting and are expected to hold a news conference Wednesday.
Russian President Vladimir Putin says enemies of the Syrian regime are responsible for the attack in which 89 people died, including children.
Secretary of State Rex Tillerson, after meeting with Russian President Vladimir Putin on Wednesday, said relations between the countries are 'at a low point'.
But Mr Tillerson fired back that "There is a low level of trust between our two countries". "The world's two foremost nuclear powers can not have this kind of relationship".
The U.S. and other countries have alleged that the chemical strike on Syria's Idlib Province that killed more than 80 civilians was carried out by the Syrian regime.
Russia's deputy United Nations envoy, Vladimir Safronkov, said the draft resolution laid blame prior to an independent investigation.
Looking at the resolution's supporters sitting around the horseshoe-shaped table in the Security Council, Safronkov said: "You are afraid of an impartial investigation".
Syrian authorities have repeatedly denied using any chemical weapons.
"The longer-term status of President Assad will be decided by the Syrian people", Tillerson had said, when asked whether the US would get involved in Syria's internal politics on March 30. The Russians operate drones in the area routinely so the Pentagon can not be certain the drone operator even knew what was happening, but the drone was a Russian asset. But we might get some clarity about United States intentions.
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Others said the statements should clear up any doubts about U.S. -Russia relations.
China, which has vetoed six resolutions on Syria since the civil war began, abstained from the vote, along with Ethiopia and Kazakhstan.
The chill in Moscow today was a far cry from the atmosphere a year ago. A nationwide TV channel Zvezda declaring ominously on Tuesday night that "only a demonstration of force" could stop Trump in Syria.
Trust between Russia and the U.S. has degraded under the Trump administration, Russian President Vladimir Putin stated.
And the president delivered a ringing reaffirmation of the North Atlantic Treaty Organisation alliance, which he had once declared "obsolete". Trump himself accused Putin of backing "an animal" and "a butcher", someone who is "truly an evil person".
"I think it's certainly possible. It's very bad for this world", Trump told Fox Business News.
Tillerson said he wanted to out an end to the "steady degradation" of friendship between Russian Federation and the United States. "We hope that the USA president will become aware of that analysis", he said Thursday. "We have already seen all of this".
MARGARET WARNER: Tensions are over more than Syria.
"If the regime is innocent, as Russian Federation claims, the information requested in this resolution would have vindicated them". Russia wants the U.S.to eliminate sanctions on Moscow related to its 2014 annexation of Ukraine's Crimea region and support for pro-Russian separatists in eastern Ukraine.
Tuesday, the White House declassified a US intelligence report that accused Putin of a cover-up to "confuse" and "obfuscate" on behalf of Assad. The two men did agree to establish a working group to try to stabilize relations.
For the PBS NewsHour, I'm Margaret Warner.




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