"There should no longer be any questions respecting the complexity of Rare Earth products," Trump wrote on social media.
"Our respective teams will be meeting shortly at a location to be determined."
Trump and a Chinese government summary of the meeting said the leaders had invited each other to their respective countries at a future date.
"The US side should take a realistic view of the progress made and withdraw the negative measures imposed on China," the Chinese government said in a statement published by the state-run Xinhua news agency.
"Xi Jinping welcomed Trump's visit to China again, and Trump expressed his sincere gratitude."
The highly anticipated call came amid accusations between the US and China in recent weeks over "rare earths" minerals in a dispute that has threatened to tear up a fragile truce in the trade war between the governments of the two biggest economies.
The countries struck a 90-day deal on May 12 to roll back some of the triple-digit, tit-for-tat tariffs they had placed on each other since Trump's January inauguration.
Although stocks rallied, the temporary deal did not address broader concerns that strain the bilateral relationship, from the illicit fentanyl trade to the status of democratically governed Taiwan and US complaints about China's state-dominated export-driven economic model.
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, who say the uncertainty has made it difficult to forecast market conditions.
China's decision in April to suspend exports of a wide range of critical minerals and magnets continues to disrupt supplies needed by car makers, computer chip manufacturers and military contractors around the world.
China's government sees mineral exports as a source of leverage - halting those exports could put domestic political pressure on the Republican US president if economic growth sags because companies cannot produce mineral-powered products.
The 90-day deal to roll back tariffs and trade restrictions is tenuous.
Trump has long pushed for a call or a meeting with Xi but China has rejected that as not in keeping with its traditional approach of working out agreement details before the leaders talk.
Trump had declared one day earlier that it was difficult to reach a deal with Xi.
"I like President XI of China, always have, and always will, but he is VERY TOUGH, AND EXTREMELY HARD TO MAKE A DEAL WITH!!!" Trump posted on Wednesday on his social media site.
The US president and his aides see leader-to-leader talks as vital to sort through log-jams that have vexed lower-level officials in difficult negotiations.
with AP
