China presents itself as a neutral party in the war and says it is not sending lethal assistance to either side, unlike the United States and other Western nations.
But China is a close political and economic ally of Russia, and NATO members have branded Beijing a "decisive enabler" of the war.
Beijing's foreign ministry said the pair held talks in the city of Guangzhou, with spokeswoman Mao Ning telling journalists they "exchanged views on the Ukraine crisis".
"Although the conditions and timing are not yet mature, we support all efforts that contribute to peace and are willing to continue to play a constructive role for a ceasefire and the resumption of peace talks," she said.
"China has always been firmly committed to promoting a political solution to the crisis," she added.
In a statement, Kuleba said Ukraine "also wants to follow the path of peace, recovery, and development".
"I am convinced that these are the strategic priorities that we share," he said, adding "Russian aggression has destroyed peace and slowed down development".
Kuleba is the first senior Ukrainian official to visit China since Russia invaded Ukraine in February 2022.
His trip is scheduled to last until Friday.
- 'Political settlement' -
China has sought to paint itself as a mediator in the war, sending envoy Li Hui to Europe on multiple rounds of "shuttle diplomacy".
President Xi Jinping told Hungary's Viktor Orban this month that world powers should help Russia and Ukraine restart direct negotiations.
Orban's visit to Beijing was branded as a "peace mission". China also released a paper last year calling for a "political settlement" to the conflict.
However, it was criticised by Western countries for enabling Russia to retain much of the territory it has seized in Ukraine.
Beijing has rebuffed claims it is supporting Russia's war effort, insisting last week that its position was "open and above board" and accusing the West of fuelling the conflict through arms shipments to Kyiv.
China did not attend a peace summit in Switzerland last month in protest against Moscow not being invited.
- 'Extract a price' -
Ukrainian President Volodymyr Zelensky called during that summit for Beijing to engage seriously with developing peace proposals.
Kuleba said on arrival in China Tuesday that "we must avoid competition between peace plans."
And he urged China to "look at relations with our country through the prism of its strategic relations with Europe".
Alexander Gabuev, director of the Carnegie Russia Eurasia Center, told AFP that Kyiv was likely to seek this week to "convince China that it should participate in a second peace summit".
"Beijing can try to extract a price, even for sending somebody like special envoy ambassador Li Hui," he said.
China has offered a critical lifeline to Russia's isolated economy since the conflict began.
But that economic partnership has come under close scrutiny from the West in recent months, with Washington vowing to go after financial institutions that facilitate Moscow's war effort.
The United States and Europe have also accused China of selling components and equipment necessary to keep Russia's military production afloat.
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