The ongoing bilateral discussions include where to sign the "phase one" agreement to resolve some of the issues that prompted Trump to impose tariffs on more than $350 billion worth of Chinese goods.

Trump said he was reluctant to say where the meeting could be held, before the two sides had reached an agreement. "But it could be Iowa or farm country or someplace like that," Trump said, adding he was certain "it will be in our country."

Some analysts question whether Xi would agree to U.S. location unless it's part of an official state visit. But Iowa is the home state of the U.S. ambassador to China, Terry Branstad, who was governor there from 1983 to 1999 and again from 2011 to 2017.

In addition, Xi visited Iowa in 1985 as an up-and-coming Communist Party official to learn about agriculture, and then again in 2012, as a guest of the Obama administration and Branstad, when Xi was China's vice president.

China has retaliated on about $110 billion of U.S. exports in response to Trump's tariffs, and both countries are expected to roll back some of those as part of a phase one deal.

A person who spoke with Trump on Thursday night told POLITICO the president remains confident that some kind of deal could be worked out, but discussions haven't concluded. There also has been internal disagreements in the administration against going easy on China.

The White House made a conscious decision not to push back on any of the stories coming out of Beijing because they view the Chinese comments as generally positive and favorable, the person said, adding that Trump wants the deal done later this month.

On Thursday, a Chinese Commerce Ministry spokesperson said the two sides had agreed in principle on a rollback in tariffs as part of a "phase one" deal, although analysts cautioned that were still many difficult issues to resolve before duties between the two countries are removed.

The editor for Global Times, a daily paper controlled by China's Communist Party, viewed Trump's latest comments favorably. "It's not a flat denial," the editor, Hu Xijin, wrote on Twitter. "What's certain is that if there's no rollback of tariffs, there will be no phase 1 deal."

On Friday, White House trade adviser Peter Navarro in an email addressed "To the Fourth Estate" took issue with some of Thursday's coverage.

"Too many journalists are getting the China trade stories wrong," Navarro said. "A major problem appears to be an over-reliance on anonymous sources with ulterior motives and without direct knowledge of the negotiations."

For its part, POLITICO asked both the White House and the Office of the U.S. Trade Representative to confirm whether the Chinese Commerce Ministry statement was correct. Neither provided any comment on the record, but they also didn't make any effort to contradict the remarks.

Still, Navarro complained that "yesterday’s misleading (and market moving) coverage of the 'tariff rollback' story was one of the worst examples [of China trade coverage] to date. The story began with a declaration by propagandists within the Chinese government that the U.S. had agreed to a 'phased cancellation' of the tariffs and that 'tariffs already increased should be canceled at the same time and by the same rate.'"

"This claim was simply false," Navarro said. "There was no such agreement — yet the story was splashed all over newspaper headlines and cable news chyrons as if it had been confirmed by reliable U.S. sources."

Ben White contributed to this report.