Trump said then that China would restart large purchases of US agricultural commodities, and the United States would ease some export restrictions on Chinese telecom equipment giant Huawei Technologies.
But sources familiar with the talks and China trade watchers in Washington say the summit did little to clear the path for top negotiators to resolve an impasse that caused trade deal talks to break down in early May.
A USTR spokesman said the call was expected this week, but gave no further details.
The United States is demanding that China make sweeping policy changes to better protect American intellectual property, end the forced transfer and theft of trade secrets and curb massive state industrial subsidies. At stake, US officials say, is the dominance of the high-tech industries of the future, from artificial intelligence to aerospace.
"We've had a change in atmospherics," said Derek Scissors, a China expert at the American Enterprise Institute, a business-oriented Washington think tank. "While this is great for markets, the administration has not said one specific thing about how we're unstuck."
Scissors, who has at times consulted with Trump administration officials, said that both sides got what they wanted out of the summit -- a lowering of the temperature and the avoidance of new tariffs that would have been painful for both sides.
Watch: US-China trade friction hurting world economic chain: Chinese scholars
One of the sources said Trump raised the issue of agricultural purchases twice during the meeting, but Xi only agreed to consider purchases in the context of a broader final agreement.
Other than a small purchase of American rice by a private Chinese firm, no purchases have materialized. Chinese officials and state media accounts in the past week have emphasized that any deal, including agricultural purchases, is dependent on the removal of US tariffs.
"The Chinese have been clear they didn't promise anything," said one source familiar with the talks.
"The idea they would give up their main leverage before getting anything doesn’t make sense. I could see them buying some pork and buying some soybeans, but it's still going to be pennies."
Trump administration officials have also downplayed the extent of pledges to allow Huawei to purchase US technology products, with White House trade adviser Peter Navarro saying that only "lower-tech" US semiconductors could be made available for sale to the company. [nL2N243133].
Reuters reported last week that the Commerce Department's export control enforcement staff was told to continue to treat Huawei as a blacklisted entity as the department considers requests for licenses to US firms to sell products and services to Huawei [nL2N24402Y]
Chinese officials point out that they only got the United States to concede on Huawei at the Osaka talks, rather than on their other demand, which was removing the existing tariffs.
So the focus on the upcoming talks will be the scrapping on the tariffs, they say.
A second source said that US tariffs on $250 billion worth of Chinese goods and Chinese tariffs on $160 billion worth of US goods could wind up being "the new normal."
One Chinese official familiar with the situation said that trade talks would be re-started very quickly, but that there was a "fairly large gap" in the core demands of both countries and it would be a challenge to reach consensus on the toughest issues.
"The negotiating environment is even more severe," the official said.
Another official said China remained concerned about the presence of hawks in the US team, such as Trump advisor Peter Navarro.
"There are bullies there," the official said.
The officials spoke to Reuters on condition of anonymity.
China's foreign ministry cited Xi as telling Trump at Osaka that "on issues concerning China's sovereignty and dignity, China must safeguard its core interests".
A senior Beijing-based Asia diplomat said there would be pressure on China's leadership not to give in to the United States and for any outcomes to seen as equal and balanced.
"A trade deal cannot be portrayed as a victory for the United States," the diplomat said, citing conversations with Chinese officials.
There has been no indication the two sides will resume negotiations using a text that had been largely agreed before China backtracked on commitments in early May, prompting Trump to proceed with a long-threatened tariff hike to 25 per cent on a $200 billion list of Chinese imports.
Beijing had cut out of that text commitments to make changes to its laws reflecting reform pledges, arguing that this would violate its national sovereignty.
Lighthizer has insisted on legal changes to make it more likely that Chinese reform pledges will be carried out.
Finding a way around this issue is paramount for talks. Beyond that, there are many other difficult issues to resolve, including the structure of an enforcement mechanism designed to hold the two sides to their pledges.
US demands for curbs to provincial and local subsidies for Chinese state companies, access to China's cloud computing market, agricultural biotech approvals and the ultimate size of China's purchases of agricultural products are all divisive issues for the two sides.
Claire Reade, a former China trade negotiator at USTR who is now a Washington-based trade lawyer with the firm Arnold and Porter, said there was room on both sides to get a deal.
"It's a question of political will and there are ways to manoeuvre around the current red flags that have been put in the ground," Reade said. "Both President Xi and President Trump have to come out of this saying they stood strong, and they in-effect got a win."
One way for China to avoid the appearance of giving in to US demands is to take some legal steps on key issues before the deal is agreed. That way they can say they’re doing it on their terms, she added.
A US official said last week the discussions were expected to resume with a phone call between US Trade Representative Robert Lighthizer, Chinese Vice Premier Liu He and Treasury Secretary Steven Mnuchin.