Mr Trump and Mr Xi were previously expected to hold a summit at the U.S. president's Mar-a-Lago property in Florida this month, but no concrete plans have been made in more than two weeks.
Later, at a Saint Patrick's Day celebration in the White House with the Irish Prime Minister Leo Varadkar, Trump predicted results in the near future.
For now, Beijing made no reference to a Trump-Xi summit at the Mar-a-Lago Such summit is unlikely to happen this month.
Trade negotiations between China and the US left investors grappling.
Chinese officials have also bristled at the appearance of the deal being one-sided, and are wary of the risk of Trump walking away even if Xi were to travel to the US.
The Trump administration is discussing a thick tome of ideas with Chinese officials as the two sides seek a trade deal, with Washington expecting some elements to be resolved soon, a top administration official said, Trend reports referring to Reuters.
U.S. President Donald Trump said on Thursday that whether a trade deal can be reached with China would probably be known in the next three or four weeks.
For the record, I think the pause in tariffs is a good thing because tariffs are a bad idea in the first place. "If it's not a deal that's a great deal for us, we're not going to make it".
Trump himself has dialed down the urgency of getting a deal signed as early as this month.
"We're doing very well with China talks", Trump told reporters at the White House on Thursday as he sat down to meet Irish Prime Minister Leo Varadkar. It's got to be the right deal, and it's got to be a good deal for us. "But it doesn't matter that much".
Boeing Co, the single largest United States exporter to China, slipped 1 per cent.
The negotiations have zeroed in on the phasing out of joint-venture requirements, the deal's enforcement mechanism and the lifting of tariffs the two sides have imposed on each other, the people familiar with the talks said.
Shares of Yum China added 0.34 percent, the only advancer in the top 10 stocks. Lighthizer warned "major issues" remained outstanding in talks.
As to the reason why China and the USA are postponing the signing of the agreement that will put an end to the trade war, Trump's trade representative Robert Lighthizer said that there are still some major issues to resolve including the intellectual property dealing.
"As to whether or not we'll strike a final deal, that I would never want to say", Trump said on Thursday.