"This is a very aggressive and unconstructive rhetoric, unfortunately," TASS News Agency quoted the spokesman as saying to reporters at a briefing on Friday.
"Any hints of an ultimatum are absolutely unacceptable to us," Peskov added
He reiterated that Moscow will not heed such claims, saying that despite existing differences, Russia hopes the US will demonstrate "political will" to continue mutually beneficial communication.
"We hope that alongside a huge number of disagreements and differences in approaches to key issues, grounds for cooperation will still remain," Peskov said.
In his first major foreign policy speech after taking office last month, Biden on Thursday demanded that Navalny be freed.
"The politically-motivated jailing of Alexei Navalny and the Russian efforts to suppress freedom of expression and peaceful assembly are a matter of deep concern to us and the international community," Biden said.
"He should be released immediately and without condition."
The President added that the US would not hesitate to "raise the cost on Russia" over the incident.
Navalny, a harsh critic of the Russian government, was detained on January 17 upon his landing at a Moscow airport from Germany, where he had received medical treatment for alleged poisoning over the past few months.
His detention sparked ongoing mass protests in major Russian cities, including capital Moscow, St Petersburg, Novosibirsk, Yakutsk, Omsk and Yekaterinburg.
In a related development also on Friday, the Russian Foreign Ministry declared a Swedish, a Polish and a German diplomat personae non grata due of their participation in the January 23 "unauthorized rallies" in Moscow and St. Petersburg.
"In compliance with the Vienna Convention on Diplomatic Relations of April 18, 1961, diplomats who took part in unauthorized rallies have been declared personae non grata. They must leave Russia as soon as possible," the TASS News Agency quoted the Ministry as saying in a statement.
The diplomats were summoned to the Ministry earlier in the day.
"The Russian side expects that Sweden's, Poland's and Germany's diplomatic missions and their personnel will strictly abide by international law," the statement added.