The Russian leader on Thursday called it "acceptable" for the country to become a "platform" for dialogue over the conflict, which US President-elect Donald Trump has said he could end after he takes office in January, France 24 reports.
That prospect has raised concerns in Kyiv that a settlement could be imposed on terms favourable to Moscow, as Ukraine struggles on the battlefield.
"If someone wants to organize peace talks in Slovakia, we will be ready and hospitable," the country's Prime Minister Robert Fico posted late Friday on Facebook.
Earlier, Slovakia's Foreign Minister Juraj Blanar said on Facebook: "We offer Slovak soil for such negotiations."
The moves come nearly three years after the start of the full-scale Russian assault on Ukraine.
Putin announced Thursday that Slovakia had offered to be a "platform" for possible peace talks and that Russia was "not against it", praising Bratislava's "neutral position".
But Putin reiterated his vow that his country would achieve "all the objectives in Ukraine".
