Both leaders expressed optimism as they and top aides sat down at a long hotel table in Buenos Aires, just before Trump was due to board Air Force One for Washington after attending the summit of G20 countries.

"We will probably end up ending up getting something that will be good for China and the United States," Trump said, while Xi said they shared tremendous responsibility to find a solution.

"Only with cooperation between us can we serve the interest of both peace and prosperity," Xi said.

The meeting, brought forward by an hour from its original time, may have been tacked on to the end of two days of G20 diplomacy, but it was in many ways the main event of the weekend.

Trump has already imposed tariffs on more than $250 billion in Chinese goods -- about half of the total imported into the United States each year -- in an attempt to pressure Beijing to change its trade rules.

Duties of 10 percent currently on most of those goods are shortly set to rise to a whopping 25 percent if a deal isn't reached.

And that's not all.

As Trump economic advisor Larry Kudlow said ahead of the dinner: "If things don't work out in this US-China summit meeting, he will invoke some 267 billion dollars in additional tariffs."

With US-Chinese disagreements on Trump's demands for better market access and intellectual property protections so profound, any real breakthrough was considered unlikely.

But financial markets, spooked by the potential impact on the world economy, hoped that at least some kind of truce could be declared.

German Chancellor Angela Merkel spoke for many when she urged progress, saying "we all realize that we are indirectly influenced by the fact that Sino-American economic relations do not run as smoothly as a world order needs."

- Personal chemistry factor -

Both sides certainly came prepared for serious discussion. The White House released the names of the two delegations, totaling 20 people in addition to the two leaders.

On the US side, these included advisers such as Kudlow and Treasury Secretary Steven Mnuchin, who are widely seen as wanting to cut a deal, but also hawkish advisers like Peter Navarro and US Trade Representative Robert Lighthizer.

Navarro's inclusion in particular was a surprise as he has harshly criticized China, accusing its leadership of duplicity.

Trump, as often in his diplomatic dealings, appears to consider his personal chemistry with Xi the most important factor in the success of the negotiations.

He has prided himself on building a good relationship with the Chinese leader, even though he acknowledges it may have trouble surviving.

"He may not be a friend of mine anymore but I think he probably respects me," Trump said in September.

At the dinner, however, he was more upbeat, saying that his ties to Xi were "a very primary reason" for considering a deal possible.

Trump's G20 summit was overshadowed by his abrupt decision to cancel a meeting with Russian President Vladimir Putin.

The White House said this was to show displeasure over Russia's attack on Ukrainian shipping.

However, questions about whether Trump's real motive was to avoid embarrassment about a deepening probe back home over improper links to Russia would not die down, leaving Trump hoping for good news from the China meet.