There was no immediate statement from either side when the dinner of more than two hours ended in Buenos Aires. Trump left immediately to board Air Force One for Washington, having spent two days attending the summit of G20 countries.
But both leaders had expressed optimism earlier as they and top aides sat down at a long hotel table in the Argentinian capital.
"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 lasted longer than scheduled and featured a menu of sirloin steak, caramel rolled pancakes and Argentinian wine. It 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 USD250 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 per cent currently on most of those goods are set to rise on January 1 to a whopping 25 per cent if a deal isn't reached. And that's not all.
As Trump economic advisor Larry Kudlow said in Washington 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, also attending the G20, spoke for many when she urged progress.
"We all realize that we are indirectly influenced by the fact that Sino-American economic relations are not running as smoothly as a world order needs," she said.
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 the growing crisis.
"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.
Beyond trade, Washington and Beijing find themselves increasingly entangled on hard-to-resolve issues. They include attempts to secure the denuclearization of North Korea and China's increasingly self-confident expansion of military power, especially in the South China Sea.
A successful dinner date with Xi would certainly help Trump's mood on the long flight home given his generally rocky G20 experience, where he faced difficult questions over relations with Saudi Prince Mohammed bin Salman and his abrupt cancellation of a meeting with Russian President Vladimir Putin.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)