The Secretary of State described Russia's alleged involvement in the 2016 vote as a "serious issue" and "one that we know" about. We may be at an all-time low in terms of a relationship with Russian Federation.
He said the two sides would also discuss disagreements on Syria and how to end the country's six-year civil war.
Fiercely feuding over Syria, Russian President Vladimir Putin met the top American diplomat in Moscow on Wednesday to see if they could rescue relations between the world's mightiest military powers. Tillerson is a former oil executive who was awarded Russia's Order of Friendship by Putin.
A senior Russian diplomat says the United States and Russia are again exchanging information on a hotline created to prevent midair incidents over Syria, but that the formal agreement on such exchanges has not been renewed.
Russian Federation has never publicly acknowledged any such attack by Assad's forces and has tried for the past 18 months to help him expand his authority in Syria.
Diplomats said Russian Federation came close to proposing its own resolution, which would have included language condemning the USA missile strikes in Syria last Thursday.
At Wednesday's press conference, Trump defended his decision to launch 59 missiles at the Syrian airbase in response to last weeks chemical attack in the rebel-held town of Khan Sheikhoun in Syria's Idlib, that killed over 80 people and wounding scores of others.
He did play down suggestions from some United States officials that Russian forces could have been complicit in last week's slaughter of 87 civilians in the town of Khan Sheikhun.
But he was firm that only Assad's forces could have carried out such a strike and insisted that Russian Federation must do more to help strip the regime of its chemical arsenal.
Assad dismisses claims he ordered Idlib attack as 'fabrication'
Assad's government told the organization it had a 1,300-ton stockpile of chemical weapons and chemicals used to make them.
And he declared that numerous divisions between Moscow and Washington were the result of "timebombs" left behind by former president Barack Obama's administration.
"Definitely, 100 per cent for us, it's fabrication", he said of the incident.
Asked whether the president's past criticism of North Atlantic Treaty Organisation could make for an awkward meeting Wednesday, an official said the president and Stoltenberg see "eye to eye" on the issue of more defense spending.
Putin, in a television interview ahead of the talks, was more blunt about the new chill in ties, and firmly rejected Washington's view of the Syrian attack.
"I said, "Mr President, let me explain something to you" - this is during dessert". Trump told Fox Business Network that his strikes were exclusively because Assad used chemical weapons. "That is an obvious fact". The Kremlin had previously declined to confirm Putin would meet Tillerson, reflecting the renewed tensions. It denied preferring Trump to his Democrat rival, Hillary Clinton, during the election campaign and said it would judge his administration by its actions rather than its words.
But Russia, an ally of Syria, used its powers in the United Nations to block it.
Mr Tillerson reiterated the United States view that Assad aircraft carried out the attack.
China's Ambassador to the UN Liu Jieyi said China supports the UN and the Organization for the Prohibition of Chemical Weapons (OPCW) in conducting a comprehensive, objective and impartial investigation into relevant cases.
Lavrov had greeted Tillerson with unusually icy remarks, denouncing the missile strike on Syria as illegal and accusing Washington of behaving unpredictably.
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