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The US's top diplomat said he had made clear to his counterparts they were "helping fuel the biggest threat" to European security since the Cold War.
Mr Blinken praised Beijing for making efforts in stopping supplies of the drug fentanyl reaching the US.
China remains the principal source of fentanyl for the US, which the White House has said is causing a public health crisis across the country.
Mr Blinken also stressed he felt Beijing can play a "constructive" role in the Middle East, pointing towards China using "its relationship with Iran to urge" against further escalation in its confrontation with Israel.
Relations between Washington and Beijing have been strained by China's claims over Taiwan and the South China Sea, and US export bans on advanced tech. They were further damaged by a row over a spy balloon last February.
In recent days, the US passed a law that would force Chinese-owned TikTok to sell the hugely popular video app or be banned in America - something Mr Blinken earlier revealed had not come up in his meeting with China's President Xi Jinping.
Mr Xi - who met Mr Blinken on Friday afternoon in Beijing's Great Hall of the People - agreed the two sides had "made some positive progress" since he met his US counterpart, Joe Biden, in November.
Mr Blinken said that one of the key routes for "better relations" between China and both the US and Europe would be for Beijing "or some of its enterprises" to stop providing "critical components" that help Russia make more munitions. The components include items such as "machine tools, micro-electronics, and optics".
"It's helping Russia perpetuate its aggression against Ukraine, but it's also creating a growing threat to Europe because of Russia's aggression," he explained, adding it was "helping to fuel the biggest threat to [Europe's] insecurity since the end of the Cold War".
"We've taken action already against Chinese entities that are engaged in this," he said. "And what I make clear today is that if China won't act, we will."
In his interview with the BBC, Mr Blinken said it remained important to see if the two countries could "build greater cooperation in areas where we have mutual interest", including artificial intelligence and military communications.
Lewis Musonye
