Russian Foreign Minister Sergei Lavrov said in Moscow following his talks with Tillerson that the OPCW should be allowed to carry out an "objective investigation".
"There is a low level of trust between our two countries", Tillerson said after the two-hour summit.
Tillerson again said the USA has "conclusive" evidence Syrian President Bashar al-Assad's regime planned and carried out a chemical attack on its civilians last week.
"Russia, as their closest ally in the conflict, perhaps has the best means of helping Assad recognise this reality", he told reporters.
One of Mr Lavrov's deputies was even more scathing.
He said working groups would be established to improve US-Russian ties and identify problems. Prior to the meeting, Lavrov urged Tillerson to prevent more USA bombings in Syria.
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Russian Foreign Minister Sergey Lavrov, who hosted his Iranian and Syrian counterparts at a trilateral meeting in Moscow, denounced last week's US attack on Syria as a "flagrant violation" of worldwide law and warned that any further such action would entail "grave consequences not only for regional but global security".
Ten countries voted in favor of the resolution, two voted against it, and three countries abstained.
"The world's two foremost nuclear powers can not have this kind of relationship", Tillerson said.
In another possible setback to a thaw with Moscow, Trump said on Wednesday that North Atlantic Treaty Organisation is not obsolete, as he had declared during the election campaign previous year.
"I believe that you have come at the right time". We may be at an all-time low in terms of a relationship with Russian Federation. "We'll see what happens". "Are we going to get involved with Syria?". Lavrov said a "deconfliction" hotline would be restored to avoid inadvertent collisions by the air forces of both countries in the Syrian war zones.
"Are we insisting on it? No".
"Right now, we're not getting along with Russian Federation at all, we may be at an all-time low", Trump said.
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He added it was "highly likely" the Assad regime was behind the chemical attack, which prompted the USA to attack a regime airbase in retaliation.
On April 4, a reported toxic gas attack hit the rebel-held town of Khan Sheikhoun in Syria's Idlib, killing over 80 people and wounding scores of others.
The Trump administration concluded that Assad was behind the act, and on Thursday ordered a cruise missile strike against a Syrian airbase as a "proportional response".
The official added that this is an opportunity for Russia to "move towards a resolution of the Syrian war" and that, "based on Russian interests in Syria", there is no reason to weaken Syria.
Russia's top diplomat accused the United States of carrying out an unlawful attack against Syrian President Bashar Assad's forces.
But he's learned more quickly than the last two presidents - especially Barack Obama - that Mitt Romney got it exactly right in 2012: Russian Federation is America's major geopolitical foe.
Tillerson was expected to challenge Russian Federation to distance itself from Assad and his Iranian backers and to work with Washington's Western and Arab allies to find a political solution to the conflict with Syria under new leadership.
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