TikTok has been given a 75-day extension by President Trump's executive order to comply with a statute that mandates the platform's sale or ban.
He said the US would not execute the statute signed by former President Joe Biden and ratified by Congress last year during that period.
Trump signed a number of orders on Monday night, including this one.
"I tell you what," he remarked to reporters in the Oval Office. Every wealthy individual has contacted me regarding TikTok.
When a reporter asked Trump why he changed his mind about seeking to outlaw TikTok in 2020, he said, "Because I got to use it."
He floated the possibility of a joint venture, saying he was seeking a 50-50 partnership between "the United States" and its Chinese owner ByteDance. But he did not give any further details on how that might work.
Trump also said potential new trade tariffs on China could be contingent on a deal over the platform's ownership. If Beijing rejected a deal "it would be somewhat of a hostile act", he said.
On Saturday evening, the Chinese-owned app stopped working for American users, after a law banning it on national security grounds came into effect.
It resumed services to its 170 million users in the US after Trump said he would issue an executive order to give the app a reprieve when he took office.
But on Monday it was still not available to download from the Apple and Google app stores.
The Biden administration had argued that TikTok could be used by China as a tool for spying and political manipulation.
Opponents of a ban have cited freedom of speech as a reason for keeping the platform open.
TikTok's parent company, ByteDance, previously ignored a law requiring it to sell its US operations to avoid a ban.
The law was upheld by Supreme Court on Friday and went into effect on Sunday, but the Biden White House said it would leave implementing the law to the incoming administration given the timing.
Trump had backed a ban of the platform during his first term in office.
The newly signed executive order places him at odds with many members of Congress from his own party.
On Sunday in a post on X, Republican Senator Tom Cotton said any company that "hosts, distributes, services or otherwise facilitates communist-controlled TikTok" could face hundreds of billions of dollars in fines.
Cotton said liability could stem not just from the Department of Justice, "but also under securities law, shareholder lawsuits, and state AGs [attorneys general]. Think about it".
TikTok chief executive Shou Zi Chew attended Trump's inauguration on Monday along with other big technology bosses, including Elon Musk, Mark Zuckerberg and Jeff Bezos.
Earlier on Monday, YouTube star Mr Beast posted a TikTok video of him apparently from a private jet on his way to make an official offer to buy the short video platform.
The post gave no other details about the offer, only that it would be "crazy".
Other companies, billionaires and celebrities have expressed interest in buying TikTok, including X owner Musk and an investor from the TV show Shark Tank, Kevin O'Leary.