Vladimir Putin has said he will discuss Xi Jinping's 12-point plan to "settle the acute crisis in Ukraine", during a highly anticipated visit to Moscow by the Chinese president.
"We're always open for a negotiation process," Mr Putin said, as the leaders called each other "dear friend".
China released a plan to end the war last month - it includes "ceasing hostilities" and resuming peace talks.
But on Friday the US warned the peace plan could be a "stalling tactic".
US Secretary of State Antony Blinken said: "The world should not be fooled by any tactical move by Russia, supported by China or any other country, to freeze the war on its own terms."
He added: "Calling for a ceasefire that does not include the removal of Russian forces from Ukrainian territory would effectively be supporting the ratification of Russian conquest."
China's plan did not specifically say that Russia must withdraw from Ukraine - which Ukraine has insisted as a precondition for any talks.
Instead, it talked of "respecting the sovereignty of all countries", adding that "all parties must stay rational and exercise restraint" and "gradually de-escalate the situation".
The plan also condemned the usage of "unilateral sanctions" - seen as a veiled criticism of Ukraine's allies in the West.
On Monday, a military band gave Mr Xi a warm welcome to Moscow. Mr Putin hailed China for "observing the principles of justice" and pushing for "undivided security for every country".
In return, Mr Xi told Mr Putin: "Under your strong leadership, Russia has made great strides in its prosperous development. I am confident that the Russian people will continue to give you their firm support."
Before Mr Xi's arrival, Mr Putin wrote in China's People's Daily newspaper that the two nations would not be weakened by "aggressive" US policy.
Publicly, Ukrainian leaders have been emphasising the common ground they have with China - respecting sovereignty and territorial integrity.
But privately, they have been lobbying for a meeting - or telephone call - between President Volodymyr Zelensky and Mr Xi.
The fear in Kyiv is that China's support for Russia - currently based around technology and trade - might become military, potentially including artillery shells.
"If China does move to openly supply weapons to Russia, it will in effect be taking part in the conflict on the side of the aggressor," said Oleksiy Danilov, the secretary of Ukraine's National Security and Defence Council.
It was in Beijing's interests to stabilise the relationship with Russia, with which it shares a 4,300km (2,700 mile) border, said Yu Jie, a research fellow on China at Chatham House.
Russia is a source of oil for Beijing's huge economy, and is seen as a partner in standing up to the US.
Ms Yu added that Mr Xi had just scored a diplomatic victory in mediating between Iran and Saudi Arabia, which have now resumed diplomatic ties.
This could be a chance for him to explore the opportunity to mediate between Russia and Ukraine.
On Monday evening, Mr Xi was treated to a seven-course meal including nelma fish from the Pechora River in northern Russia, a traditional Russian seafood soup and pancakes with quail - alongside Russian wine.
Presidential spokesperson Dmitry Peskov indicated there would be a "detailed explanation" of Moscow's actions in Ukraine over dinner. Russian and Chinese delegations will hold talks on Tuesday - the main day of the visit.
The meeting comes days after the International Criminal Court (ICC) issued an arrest warrant for the Russian president over war crime allegations.
This means Mr Putin could technically be arrested in 123 countries - though neither China nor Russia are on that list.
Making a trip to Moscow so soon after the ICC's announcement suggests China feels "no responsibility to hold the Kremlin accountable" for atrocities in Ukraine, Mr Blinken said.
Western leaders have been attempting since last February to isolate Russia, following its full-scale invasion of Ukraine.
But they have been unable to establish a global consensus, with China, India and several African nations reluctant to condemn Mr Putin.