Earlier Russian Foreign Minister Sergey Lavrov said after talks with his USA counterpart in Moscow that if there is not an global inquiry then it will mean that the worldwide community is not interested in establishing the truth. Lavrov swiftly asserted that Russian Federation was not convinced and called for more investigation.
The United States and its European allies imposed financial sanctions on Russian Federation in 2014 after Putin seized territory from neighboring Ukraine.
"Iran is dumping fuel on the flames of this war in Syria so it can expand its own reach", she said.
"There is a low level of trust between our two countries".
"The working level of confidence in Russian-American relations, especially at the military level, under the administration of Donald Trump, has not improved, but rather worsened".
Still, Mr Tillerson sought to stress the positives from his meetings.
Tillerson, whom Putin awarded the Order of Friendship in 2012, was perhaps best suited for the mission of reestablishing communications.
Making little to no eye contact, Tillerson and Lavrov gripped each other's hands and wore expressions that mainly ranged from grim to flat as photographers snapped photos.
A senior Russian diplomat says Moscow is opposing the latest version of a Western draft UN Security Council resolution on a chemical weapons attack in Syria. "We believe it is of principal importance to prevent risks of a repeat of such steps in the future".
Trump even criticized Putin on Wednesday, something he has largely left to top aides over the last several days.
Tillerson reiterated the US position that Syrian President Bashar al-Assad must eventually relinquish power in Syria, a position starkly at odds with Russian Federation.
Meanwhile, US President Donald Trump has called on North Atlantic Treaty Organisation allies to work together to resolve the disaster in the war-wracked Syria.
"The use of chemical weapons against civilians is horrific, but the fact is that President Trump's military action violates the constitution and USA treaty obligations under the United Nations charter", said Hina Shamsi, the director of the National Security Project at the American Civil Liberties Union.
"It can continue acting as a lifeline for Assad's murderous regime, or it could live up to its responsibilities as a global power, and use its influence over the regime to bring six long years of failed cease-fires and false dawns to an end", Johnson said.
Trump had called the military alliance, which is a bulwark against Russian Federation, "obsolete" while campaigning for the presidency.
Tillerson said Syria's government had committed more than 50 attacks using chlorine or other chemical weapons over the duration of the conflict.
Russian President Vladimir Putin has taken a page out of President Donald Trump's playbook by questioning the reliability of USA intelligence reports about chemical weapons usage in Syria.
"Moscow has since claimed that the release of chemicals was caused by a regime airstrike on a terrorist ammunition depot in the eastern suburbs of Khan Shaykhun".
Tillerson also said that the facts available to the United States were "conclusive" that Syrian government forces carried out the chemical weapons attack. "Our military policy in Syria has not changed".
"We have seen very alarming actions recently with an unlawful attack against Syria", Lavrov said, referring to the 59 Tomahawk missiles Trump launched at an air base to punish Assad for using chemical weapons.
The talks were a test of US-Russia relations which have been marred with questions over Syria, and alleged meddling in the US elections.
But Russia made clear it had no intention to acquiesce.
Staffan de Mistura told the U.N. Security Council Wednesday that he is ready to hold a new round of talks between the government and opposition in May but some things should be sorted out first. "They have also signaled to America's friends and foes that this administration is open to taking quick military action". But the USA says Tillerson believes all evidence points to Assad as the culprit.
Syria denied any use of chemical weapons and Moscow said the deaths had been the result of a conventional strike hitting a rebel arms depot containing "toxic substances".