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In a social media post on Sunday, Trump said he had signed an order which "directed the Presidential Working Group to move forward on a Crypto Strategic Reserve that includes XRP, SOL, and ADA".
About an hour later he added in another post: "And, obviously, BTC and ETH, as other valuable Cryptocurrencies, will be at the heart of the Reserve."
The first three coins he named jumped by up to 62% on Sunday.
Bitcoin and Ethereum also jumped by more than 10% each.
From Bitcoin to XRP: Key cryptocurrency terms and what they mean
The posts marked a new upward turn for crypto prices, which had dropped sharply since spiking after his election.
Shortly after taking office in January, Trump signed an executive to create a presidential working group tasked with proposing new crypto laws and regulations.
The order called on the group to "evaluate the potential creation and maintenance of a national digital asset stockpile" that could use "cryptocurrencies lawfully seized by the Federal Government through its law enforcement efforts".
It is unclear whether creating a new national strategic stockpile would require an act of Congress.
Trump had previously been a crypto critic, telling Fox News in 2021 that Bitcoin is a "scam".
But in recent weeks, both he and his wife Melania Trump have launched their own cryptocurrencies, leading to accusations that they are trying to profit from his White House policies.