Secretary of State Rex Tillerson met his Russian counterpart Foreign Minister Sergei Lavrov in Moscow in what he said was an attempt to narrow "areas of sharp difference".
The powers are at odds over the fate of Moscow's longtime ally President Bashar al-Assad, a rift exacerbated after an alleged Syrian chemical attack last week that triggered a punitive US missile strike.
And as the men entered a day of tense talks, Putin admitted that relations between Washington and Moscow have worsened in the three months that Trump has been in office.
Tillerson said he wanted "a very open, candid and frank exchange" with Lavrov.
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"Our meeting today comes at an important moment in our relationship so that we can further clarify areas of common objectives, areas of common interest - even where our tactical approaches may be different - and further clarify areas of sharp difference so that we can better understand why these differences exist," he said.
Lavrov said Moscow was hoping to understand Washington's "real intentions" and warned that Moscow considered it "fundamentally important" to prevent more "unlawful" US strikes against its ally Syria.
He said the visit - the first to Moscow by a senior Trump administration official - offered an opportunity to clarify the chances of cooperation "above all on the formation of a broad anti-terrorist front".
US officials have suggested Russian forces may have colluded in the latest atrocity blamed on Assad's regime, and it remained unclear if Tillerson will be invited to meet Putin.
On the eve of the talks, far from trying to calm tempers, both sides escalated their rhetoric as the US tried to prise Moscow and Damascus apart.
Putin accused Assad's opponents of planning to stage chemical attacks to be blamed on Damascus in order to lure the United States deeper into the conflict.