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.
"You can say that the level of trust on a working level, especially on the military side, has not improved but most likely worsened," Putin said in the transcript of an interview with Mir television released by the Kremlin.
Watch: Lavrov meets with Tillerson
Tillerson said he wanted "a very open, candid and frank exchange" with Lavrov.
"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.
Tillerson was expected to challenge Russia 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.
'Real intentions'
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".
Despite hopes of an improvement in ties under Trump, the Tillerson-Lavrov talks look set to be dominated by the war of words over Syria - where more than 320,000 people have died in six years of brutal war.
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.
'Where is the proof?'
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.
The Kremlin leader again slammed the US missile strike and angrily rejected the allegation that Assad's forces were behind the suspected chemical attack on the town of Khan Sheikhun that left 87 civilians dead including children.
"Where is the proof that Syrian troops used chemical weapons? There isn't any. But there was a violation of international law. That is an obvious fact," Putin told Mir.
Watch: Tillerson hopes Russia will 'abandon Syria'
Anger over Hitler comments
On the even of the Tillerson-Lavrov meeting, the White House compared Assad's tactics to those of World War II Nazi dictator Adolf Hitler, sparking widespread criticism for apparently ignoring the Holocaust.
Trump's spokesman Sean Spicer said Tillerson would go into the meeting with Lavrov to "make sure we let Russia know that they need to live up to the obligations it has made" to halt Assad's chemical weapons use.
A senior US official asked how Russian forces could not have had foreknowledge of the chemical attack.
And US Defence Secretary James Mattis said Washington has "no doubt" that Assad was behind the massacre.
He warned that the US cruise missile strike in response "demonstrates the United States will not passively stand by while Assad ignores international law and employs chemical weapons he declared destroyed".
Watch: Sean Spicer's White House gaffe
The UN Security Council is set to vote Wednesday on a resolution demanding the Syrian government cooperate with an investigation into the attack - a measure Russia will likely veto, diplomats said.
US relations with the Kremlin have become politically toxic for the White House on the back of claims Putin conspired to get Trump elected.
Tillerson, a former oil executive, might once have looked like the perfect envoy to mend strained ties, having worked closely with the Kremlin while negotiating deals for energy giant ExxonMobil.
But the underlying tensions between the former Cold War foes never went away and last week's chemical attack has left ties once again in crisis.
