"Yes, we agree with him," Russian state media quoted Peskov as saying on the sidelines of a meeting of former Soviet states in Turkmenistan.
Peskov said diplomats should find a way to move toward peace.
"The art of diplomacy precisely involves finding some way out that would allow moving onto a peaceful track," he said.
He also said the Kremlin saw no immediate prospect of a trilateral summit involving Russian President Vladimir Putin, Ukrainian President Volodymyr Zelenskyy and U.S. President Donald Trump.
Peskov reiterated Moscow's position that Russia wants a comprehensive settlement rather than temporary measures such as a limited ceasefire.
"We are not for a fragmented solution, we are for a comprehensive solution that will allow for sustainable settlement for many, many years, for decades," he said.
Rubio calls war a 'strategic stalemate'
Rubio said in an interview with Greek newspaper Kathimerini published on Oct. 8 that Russia's war against Ukraine had reached a "strategic stalemate."
"Strategic stalemates are only broken in one of two ways: through a negotiated settlement, or through escalation by one side or both that ends up spreading beyond the confines of the original conflict," Rubio said.
"Right now, there don't seem to be prospects of a negotiated settlement."
Rubio said Washington remained prepared to help facilitate talks, but added that diplomacy had so far "proved elusive."
He said Russia continues to define victory as taking all of Donetsk Oblast, while Ukraine considers that demand unacceptable.
Rubio also warned that Russia appears intent on using the coming winter to further damage Ukraine's power grid and try to force Kyiv into capitulation, while Ukraine has become increasingly effective at carrying out long-range strikes inside Russia.
Zelenskyy rejects 'stalemate' assessment
Zelenskyy rejected Rubio's characterization later on Oct. 8 during a visit to Pryluky, where a Russian missile strike on an apartment building killed 22 people, including five children.
"Even on the first day of the war, we weren't backed into a corner," Zelenskyy said.
He argued that stronger economic pressure on Moscow, sanctions and additional U.S. support could change the situation.
"You cannot, on the one hand, negotiate with the Russians about future economic projects and, on the other, say that we are in some kind of diplomatic stalemate," Zelenskyy said.
"We are not at a diplomatic stalemate."
He urged Washington to increase pressure on Russia's economy.
"Shut down their entire economy. Sew Russia's mouth shut. Stop feeding them with your sales," Zelenskyy said.
U.S. envoys Steve Witkoff and Jared Kushner are expected to meet Ukrainian representatives in Miami on Oct. 9 to discuss new proposals and work toward a common approach to ending the war, Reuters reported.