Mr Tillerson, who was previously awarded the Russian Order of Friendship from Vladimir Putin, said he was "hopeful" of positive discussions.
But he criticised Syrian dictator Bashar al-Assad, a close ally of Mr Putin, calling his regime "barbaric".
We want to relieve the suffering of the Syrian people
He said: "We want to relieve the suffering of the Syrian people. We want to create a future for Syria that is stable and secure.
"Russia can be a part of that future and play an important role, or Russia can maintain its alliance with [Syria, Iran and Hezbollah], which will not serve its long-term interests.
"But only Russia can answer that question."
Rex Tillerson arrives in Moscow for crunch talks with Russian officials
Countries that support and oppose the missile strikes in Syria
Mon, April 10, 2017
European countries have been broadly supportive so far as President Trump ordered missile strikes against a Syrian airfield from which a deadly chemical weapons attack was launched
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SYRIA OPPOSES: President Bashar al-Assad's office denounced the U.S. strike as 'reckless, irresponsible behavior.'
Tillerson speaks with US Ambassador to Russia John F Tefft
Thick black smoke decended on Moscow's Vnukovo International Airport as Mr Tillerson landed in the Russian capital this afternoon.
The fire was caused by grass and rubbish burning outside the airport, according to local media reports.
A spokesman for Russia's Foreign Ministry said it hoped the talks with the Secretary of State would be "productive".
Tillerson said the US wants to 'relieve the suffering of the Syrian people'
Today's discussions will be Tillerson's biggest challenge since being appointed as Washington's top diplomat in January.
Russia and Iran have stood firmly by Mr Assad since last week's missile strike – the first time the US has directly attacked the dictator's military.
Mr Tillerson, a former Exxon oil executive, spent this morning holding talks about Syria at a crucial G7 summit in Italy.