But Russia, an ally of Syria, blocked a draft UN Security Council resolution which would require President Assad to provide information about air operations and grant inspectors immediate access to air bases.
United Nations investigators already have the mandate under previous resolutions to look into allegations of chemical weapons use in Syria but the West had pushed for council resolution to underscore its support for a thorough investigation in the Khan Sheikhun case.
Tillerson also said Assad's rule was "coming to an end" and called on Russian Federation to help with the transition.
"Right now we're not getting along with Russian Federation at all", Mr Trump said flatly during a White House news conference with Nato Secretary-General Jens Stoltenberg.
President Trump said Wednesday that relations with Russian Federation "may be at an all-time low" following Syria's use of chemical weapons last week and the USA airstrike that followed.
It seems Putin agrees.
"You can say that the level of trust on a working level, especially on the military side, has not improved but most likely worsened", Mr Putin said in the transcript of an interview with Mir television released by the Kremlin.
The fact-finding mission was sent from the Organisation for the Prohibition of Chemical Weapons (OPCW) in The Hague to gather biometric samples and interview survivors, sources toldReuters on Thursday.
This comes after consensus from USA and world leaders that his government forces were behind the attack.
Trump's repeated claims that he could mend relations between Washington and Moscow has fuelled accusations that he secretly colluded with Russian Federation to win the United States presidential election a year ago.
But Mr Assad said it was "not clear whether it happened or not, because how can you verify a video?"
Following Donald Trump's "animal" remark for Syrian President Bashar Assad in the wake of the Idlib chemical attack, Syria's senior diplomat has come down heavily on the US President.
Assad said Syria, which is a signatory to the worldwide Chemical Weapons Convention, would accept an "impartial" chemical attack probe to investigate the accusations against him.
"A successful ouster of a dictator is for me very hard to remember", Lavrov said. "We have already seen all of this".
U.S. Central Command said Thursday that coalition aircraft were given the wrong coordinates by their partner forces, the predominantly-Kurdish Syrian Democratic Forces, for a strike meant to target Islamic State militants south of their Tabqa stronghold.
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