On Wednesday, Russia vetoed a U.N. resolution drafted by the United States, Britain and France demanding that the Syrian military provide unfettered access for UN investigators to details of their operations on the day of the alleged attack.
And shortly afterwards, Russian Federation vetoed a UN Security Council resolution that would have demanded Syrian cooperation on the investigation.
The meetings come on the heels of a USA missile strike on an air base in Syria in retaliation for a chemical weapon attack on civilians that's been blamed on the Bashar al-Assad regime.
Only minutes earlier, his counterpart, Russian foreign minister Sergey Lavrov, had claimed the two countries agreed work together on a probe of the April 4 chemical weapons attack in northern Syria that prompted retaliatory American missile strikes.
During his visit to Moscow on Wednesday, Mr Tillerson said US-Russia ties had reached a "low point" - despite a lengthy meeting with Mr Putin and Mr Lavrov.
Russia's top foreign minister said Wednesday that his country will consider reopening a phone line with the United States used to avoid aircraft collisions over Syria only if the USA agrees to stop attacking Syrian government targets.
Assad has nonetheless denied responsibility.
Finally, the New York Times reports that Trump's rapidly changing positions on Syria, Russia, and a host of other global issues are giving leaders around the world "geopolitical whiplash".
He also criticized US foreign policy, calling it "ambiguous" and "contradictory".
"I'd like to think that they didn't", Trump said during a joint press conference with NATO Secretary-General Jens Stoltenberg. "This means that they do not want success in the peace process", Muallem said during a meeting with Russian Foreign Minister Sergei Lavrov.
The day before, Tillerson had issued Moscow an ultimatum, saying it had to decide whether to side with the USA and its allies, or align itself with Assad, Hezbollah, and Iran.
U.S. Ambassador to the United Nations, Nikki Haley, called on Moscow to stop protecting Assad and said the United States wants to work with Russian Federation toward a political solution for Syria.
Mr Trump said the USA is "not getting along with Russian Federation at all" amid rising tensions between the two global powers over Syria.
Mr Tillerson said the Trump administration's position was clear: Bashar al Assad has to relinquish the presidency.
He said "it would be a fantastic thing" if the two nations got along better but cautioned that "it may be just the opposite". And Russia's credibility and reputation across the world have been poisoned by its toxic association with Assad.
"Any use of chemical weapons is unacceptable, can not go unanswered and those responsible must be held accountable", the North Atlantic Treaty Organisation chief said.
"We believe it is fundamentally important not to let these actions happen again".
He said the two sides would also discuss disagreements on Syria and how to end the country's six-year civil war.