US State Department spokesman Ned Price said that Mr Blinken “stressed the importance of continuing a diplomatic path to de-escalate tensions”.
And a US official, who spoke on condition of anonymity, said Mr Blinken’s goal was to see “if there is a diplomatic off-ramp” and “common ground” where Russia can be persuaded to pull back from Ukraine.
With tens of thousands of Russian troops massing on Ukraine’s borders, efforts have intensified to prevent tensions escalating into a new European war.
However, in a joint press conference with visiting German Foreign Minister Annalena Baerbock on Tuesday, Mr Lavrov said there would be no further negotiations until the West responds to its demands for sweeping security guarantees.
They include a permanent ban on Ukraine joining NATO.
Washington has rejected the demands.
The Russian embassy in Washington called for the US to stop provide more weapons to Ukraine or risk escalating tensions further.
While the US and its European allies have no plans to meet a Russian attack against Ukraine with military force, the economic counter-measures would be unlike any used in the past, Washington says.
The US official said it was possible that Russia is not interested in a diplomatic solution.
“I think it’s still too early to tell if the Russian government is genuinely interested in diplomacy, if it is prepared to negotiate seriously in good faith, or whether it will use discussions as a pretext to claim that diplomacy didn’t address Moscow’s interests,” the official said.
Kyiv has been battling a pro-Moscow insurgency in two breakaway regions bordering Russia since 2014, when the Kremlin annexed Ukraine’s Crimean peninsula. The conflict in eastern Ukraine has so far left more than 13,000 dead.