President Xi and Kim Jong Un have not met in person, and with no top-level diplomatic visits announced between the two countries in 2017 until this point, Pyongyang and Beijing will need time to "catch up", said Delury.
Trump also addressed South Korea's National Assembly where he issued a stark warning to North Korea.
While in Asia, President Trump spoke about North Korea on several occasions.
Trump characterised that endeavour as "tremendously successful", a description disputed by analysts who said little progress had been made on containing North Korea's nuclear program.
China is North Korea's main ally and trading partner, accounting for 90 percent of the isolated state's trade volume. He urged Xi to "work on it very hard".
The four-day joint naval exercises by the USA and South Korea, which began Saturday in waters off the South's eastern coast, were described by military officials as a clear warning to North Korea. "But past American presidents have pushed China on North Korea before, and China's never come around".
It is not clear how long Song could stay, but he has already visited Vietnam and Laos to inform them of the results of the congress, a typical courtesy China extends other communist countries after such important meetings.
While the department traditionally briefs Communist allies after the party congress, the timing suggests Song may be carrying a message from the Xi-Trump talks. So the briefing aspect is largely a formality.
He said he had a candid conversation with Chinese President Xi Jinping about the USA trade deficit with China and said the United States 'can no longer tolerate unfair trading practices that steal American jobs, wealth and intellectual property'. So flashy breakthroughs on that front aren't likely.
They hoped the North could freeze its nuclear missile programmes in exchange for the United States and South Korea halting the military drills Kim considers as preparation for invasion.
Trump said at all the summits and throughout the trip, he asked all nations to support his campaign of "maximum pressure" for North Korean denuclearisation.
Trump said in a tweet on Sunday that Kim had insulted him by calling him "old" and said he would never call the North Korean leader "short and fat".
Officials in the North Korean government are reportedly "trying to figure out" if Donald Trump is "crazy" or if his increasingly provocative stance against the rogue state is "just an act", a U.S. negotiator with Pyongyang has said.