Xi's three-day trip also serves as a show of support for internationally isolated Putin, just days after a war crimes tribunal issued a warrant for his arrest over accusation of unlawfully deporting Ukrainian children.
"We are always open to negotiations," Putin told the Chinese leader, who was on his first visit to Moscow since the start of Russia's military intervention in Ukraine last year.
The United States has accused Beijing of mulling arms exports to Moscow -- claims China has vociferously denied.
US Secretary of State Antony Blinken voiced skepticism over Xi's Ukraine proposals, warning they could be a "stalling tactic" to help Russia.
"Russia alone could end its war today. Until Russia does, we will stand united with Ukraine for as long as it takes," Blinken said later in a statement.
Xi and Putin came together in part to discuss China's 12-point position paper on the Ukraine conflict, which includes a call for dialogue and respect for all countries' territorial sovereignty.
During his initial meeting with Putin, Xi hailed "close ties" with Russia and the Russian leader said the two countries had "plenty of common objectives and tasks".
State news agency RIA Novosti said talks between the Russian and Chinese leaders lasted four and a half hours.
The two will meet again for formal talks on Tuesday.
Putin has welcomed Beijing's statements on Ukraine as being indicative of a willingness to play a "constructive role" in ending the conflict.
But Kyiv on Monday reiterated calls for Russia to withdraw its forces from Ukraine.
"We expect Beijing to use its influence on Moscow to make it put an end to the aggressive war against Ukraine," Ukrainian foreign ministry spokesman Oleg Nikolenko said in comments sent to AFP.
The head of Russia's Wagner mercenary group said Monday that his forces control more than two-thirds of the embattled eastern Ukraine town of Bakhmut -- scene of the longest battle of Russia's offensive.
"At the moment, Wagner units control around 70 percent of the city of Bakhmut and are continuing operations to complete the liberation of the city," Yevgeny Prigozhin said in an open letter to Russian Defence Minister Sergei Shoigu.
A day before Xi's arrival, a defiant Putin went to the Russian-held Ukrainian city of Mariupol -- his first visit to territory captured from Kyiv since Moscow's forces pushed across the border in February 2022.
'Objective and impartial'
Xi's visit also comes just days after the International Criminal Court (ICC) issued an arrest warrant for Putin on the accusation of unlawfully deporting Ukrainian children.
Beijing said Monday the ICC should avoid what it called "politicization and double standards" and respect the principle of immunity for heads of state.
Russia said it had opened a criminal probe into ICC prosecutor Karim Khan, saying he had accused "a person known to be innocent" and was planning "an attack on a representative of a foreign state enjoying international protection".
Beijing and Moscow have drawn closer in recent years under a partnership that has served as a diplomatic bulwark against the West.
China has lambasted what it sees as a US-led pressure campaign against Russia as Moscow's military effort in Ukraine drags on, instead calling for what it calls "impartial" mediation of the conflict.
"No single country should dictate the international order," Xi wrote in a Russian newspaper article published on Monday.
Beijing's stance has drawn criticism from Western nations, which say China is providing diplomatic cover for Moscow's armed intervention.
They argue that China's proposals are heavy on grand principles but light on practical solutions.
In Brussels, EU ministers agreed Monday on a two-billion-euro plan to raid their own arsenals and jointly purchase desperately needed ammunition for Ukraine.
The European defense and foreign ministers backed an initiative aimed at providing Ukraine with one million artillery shells in the next 12 months as well as replenishing EU stocks.
Meanwhile the United States announced $350 million in new military aid to Ukraine, including ammunition for Himars rocket launchers.
Analysts say Xi's moves are unlikely to yield a cessation of hostilities, but his trip will be closely watched in Western capitals.
The Wall Street Journal has reported that Xi could also be planning his first call with Ukrainian President Volodymyr Zelensky since the conflict began.
Zelensky has said he would welcome talks with his Chinese counterpart.
© Agence France-Presse