The call came days after negotiators from Russia and Ukraine met to discuss a US-brokered plan to end the war -- nearly four years after Moscow's invasion -- which Western governments accuse Beijing of enabling.
"China is willing to work with Russia to ... strengthen strategic coordination, enrich the substance of cooperation, improve exchange mechanisms," Dong told his Russian counterpart Andrey Belousov, according to CCTV.
Dong also said the two countries should "jointly enhance the ability to respond to various risks and challenges and join hands to inject positive energy into global security and stability".
There was no mention of the Ukraine conflict in the readout reported by CCTV or in a statement from Russia's defence ministry.
"Since our last meeting in June of last year, many events have occurred that have significantly affected the international situation," Belousov was quoted as saying in the statement.
"The examples of Venezuela and Iran require our agencies to continuously analyse the security situation and take appropriate action," he added.
Belousov also said the meeting would "further strengthen our bilateral strategic partnership".
China and Russia are close partners, and while Beijing has said it takes a neutral stance on the war in Ukraine, it has never condemned the invasion.
Western governments accuse Beijing of providing Russia with crucial economic support for its war effort, notably by supplying military components for its defence industry.
Russian and Ukrainian negotiators held a two-day meeting in Abu Dhabi on Friday and Saturday to discuss a peace plan pushed by US President Donald Trump.
Trump has also pointed to the threat of Chinese and Russian influence in the Arctic as part of the reason for his desire to acquire Greenland.
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