President Donald Trump's failure to reach a nuclear agreement with North Korea actually brings Washington and Beijing closer, according to Blackstone Chairman and CEO Steve Schwarzman, who has close economic ties with China.

Despite the high stakes economic battle between the United States and China, Beijing's top concern is North Korea's nuclear policy, the private equity billionaire said Thursday on CNBC's "Squawk Box."

"When you talk to the Chinese about North Korea, they think that if anything goes wrong on that peninsula there's nuclear waste that's going to come into China," Schwarzman said. "That is their number 1 concern. They would like a denuclearized North Korea. To the extent it didn't happen, [it] actually moves the countries together, China and the U.S."

Schwarzman, who had been chairman of one of Trump's business advisory councils before they were disbanded, said the U.S. and China want to "accomplish the same thing" with North Korea, but so far neither party have been able to do it.

Trump, who was pushing North Korea to give up its nuclear weapons, said Thursday he cut short his summit with North Korean leader Kim Jong Un because the two sides could not agree on the removal of economic sanctions against Pyongyang. Trump described the talks as "productive," but he did not commit to a third summit with the dictator.

The turn of events defied expectations. Trump, who was at the summit in Vietnam as his former personal lawyer gave explosive testimony against him at a House hearing, could have touted a win on the international stage by producing some sort of deal with North Korea, experts said.

Trump's negotiations with Kim also came as China and the U.S. try to resolve their trade disputes under a tariff cease-fire. China, the world's second-largest economy, has long said it supports a nuclear-free Korean Peninsula.

Schwarzman does not expect Trump's failed talks with North Korea will have an negative impact with China. "Don't overread where the game is now," he added.

Schwarzman, whose firm has $472 assets under management, headed Trump's strategic and policy forum. The CEO advisory group was dissolved following an uproar over remarks the president made about the August 2017 white supremacist rally in Charlottesville, Virginia.

-- CNBC's Everett Rosenfeld contributed to this report.