Beijing, for its part, said it hoped Washington would meet halfway to settle a bitter trade feud that, along with signs of a global slowdown, has loomed over a two-day Group of 20 summit that began in Japan's western city of Osaka.
China and the United States are locked in a trade dispute and expectations have dimmed that Trump and Xi can ease tension when they meet on the sidelines of the meeting.
"At a minimum it will be productive. We’ll see what happens and what comes out of it," Trump told reporters after a series of meetings with leaders where he made clear that his priority was two-way trade deals to boost the US economy.
Asked, however, if he had promised Xi a six-month reprieve on imposing new tariffs on a $300 billion list of nearly all remaining Chinese imports, Trump said "No".
Trump has imposed tariffs on $250 billion of Chinese imports and is threatening to extend those to another $300 billion of goods, effectively everything China exports to the United States. China has retaliated with tariffs on US imports.
Asian shares stumbled and gold slipped on Friday, as doubts grew that the highly anticipated meeting of the leaders of the world's two biggest economies would bring progress in resolving their dispute.
In Beijing, foreign ministry spokesman Geng Shuang said, "We hope the US side can meet China halfway and work hard together to ensure the meeting achieves positive results.
"This accords with the interests of both countries and is what the international community is hoping for," he told a news briefing.
Threat to global growth
Trump's administration also has trade feuds with India and Japan, whose leaders he met on Friday.
Trump said he saw US trade prospects improving, days after criticising the US-Japan security treaty and demanding that India withdraw retaliatory tariffs.
"I think we’re going to have some very big things to announce. Very big trade deal," Trump said before he began talks with Indian Prime Minister Narendra Modi, but gave no details.
A White House official said the two leaders had called on their teams to work on mutually beneficial trade solutions.
Trump also made a push to discuss US concerns about Chinese telecoms equipment maker Huawei.
The United States has pressed its allies to shun Huawei in their fifth generation, or 5G, networks on security grounds, and it has also suggested it could be a factor in a trade deal with Xi.
"We actually sell Huawei many of its parts," Trump said at his meeting with Modi. "So we’re going to be discussing that and also how India fits in. And we’ll be discussing Huawei."
Several leaders warned that the growing trade friction was threatening global growth.
"The trade relations between China and the United States are difficult, they are contributing to the slowdown of the global economy," European Commission President Jean-Claude Juncker told a news conference.
Xi also warned about the protectionist steps he said some developed countries were taking.
"All this is destroying the global trade order ... This also impacts common interests of our countries, overshadows peace and stability worldwide," Xi told a gathering of leaders of the BRICS grouping on the sidelines of the G20 meet.
Reforming world trade rules
Modi, at the same meeting, called for a focus on reforming the World Trade Organization (WTO) and Russian President Vladimir Putin decried what he called efforts to destroy the Geneva-based body.
"We consider counter-productive any attempts to destroy WTO or to lower its role," Putin said.
The situation of the global economy was worrying, as trade felt the effect of "protectionism (and) politically motivated restrictions", he added.
Russian Economy Minister Maxim Oreshkin said there was no agreement on how to reform the WTO system, whose rules Washington believes are outdated, though a Japanese official said G20 members agreed on the importance of reform.
The G20 leaders were also struggling to find common ground on issues such as information security, climate change and migration, said Svetlana Lukash, a Russian official helping to coordinate the meetings.
Trump, who often castigates trading partners on Twitter and at raucous political rallies, put a positive spin on trade developments with Japan.
"I appreciate the fact that you're sending many automobile companies into Michigan and Ohio and Pennsylvania and North Carolina," Trump told Japanese Prime Minister Shinzo Abe, listing US states key to his re-election effort next year.
Japan and the United States are engaged in difficult trade talks as Trump's administration looks to cut the US trade deficit.
Abe called his frequent meetings with Trump "proof of the strong US-Japan alliance", days after the US leader renewed his criticism of the US-Japan security treaty as unbalanced.
Abe later urged G20 leaders to send a strong message in support of free and fair trade, warning that trade and geopolitical tensions were rising and downside risks to the global economy prevailed.
"Today, I want to discuss with leaders measures to further enhance momentum towards reform in WTO," he said.
Japanese and US officials will meet early next month to accelerate progress toward a trade deal, Economy Minister Toshimitsu Motegi told reporters after meeting US Trade Representative Robert Lighthizer, but added that they did not discuss a target date.
This story has been published from a wire agency feed without modifications to the text. Only the headline has been changed