Asked by a reporter aboard Air Force One whether Xi had agreed to do so, Trump replied: "Yes, he did."
The Chinese embassy in Washington did not immediately respond to a request for comment.
Trump's comment came one day after a rare call with Xi aimed at resolving trade tensions that have been brewing over the topic for weeks.
At that time, Trump said there had been "a very positive conclusion" to the talks, adding that "there should no longer be any questions respecting the complexity of Rare Earth products."
In another sign of easing tensions over the issue, China has granted temporary export licenses to rare-earth suppliers of the top three U.S. automakers, two sources familiar with the matter said.
The U.S. president's top aides are set to meet their Chinese counterparts in London on Monday for further talks.
"We're very far advanced on the China deal," Trump told reporters on Friday.
The countries struck an agreement on May 12 in Geneva, Switzerland, to roll back for 90 days most of the triple-digit, tit-for-tat tariffs they had placed on each other since Trump's January inauguration. Financial markets that had worried about trade disruptions rallied on the news.
Rare earths and other critical minerals are a source of leverage for China as Trump could come under domestic political pressure if economic growth sags because companies cannot make mineral-powered products.
Since returning to the White House in January, Trump has repeatedly threatened an array of punitive measures on trading partners, only to revoke some of them at the last minute. The on-again, off-again approach has baffled world leaders and spooked business executives.
