Trump ordered that the Justice Department should not enforce the law's provisions for 75 days.
The extension allows time for negotiations over a business deal that could keep TikTok available in the US.
Under US law, TikTok's Chinese parent company, ByteDance, was required to divest from the app by Sunday, or risk a ban.
TikTok CEO Shou Zi Chew attended Trump's inauguration, along with other tech bosses. (AP PHOTO)
However, Trump expressed confidence that with the extension, a deal could be reached that would benefit both sides.
"I guess I have a warm spot for TikTok," Trump said.
Shou Zi Chew, TikTok's CEO, attended Trump's inauguration earlier in the day, seated with American tech heavyweights.
Trump has amassed nearly 15 million followers on TikTok since he joined last year, and he has credited the trendsetting platform with helping him gain traction among young voters.
Yet its 170 million US users could not access TikTok for more than 12 hours between Saturday night and Sunday morning.
The platform went offline before the ban approved by Congress and upheld by the US Supreme Court took effect on Sunday.
After Trump promised he would pause the ban Monday, TikTok restored access for existing users. Google and Apple, however, still have not reinstated TikTok to their app stores.
During the signing of the order in the White House on Monday, Trump outlined a proposal for the US to acquire a 50 per cent stake in TikTok, describing it as a fair price to ensure the app's continued access to the US market.
Without US approval, Trump claimed, TikTok would be "worthless".
Trump said that he could either facilitate the sale or ensure the app's shutdown in the country.
"I tell you what. Every rich person has called me about TikTok," Trump said.
He downplayed privacy concerns, stating there were "bigger problems" than data about young TikTok users being accessed by China.
The law behind the potential ban was introduced over fears that the Chinese government could exploit TikTok's vast data to manipulate public opinion in the US. TikTok rejects this claim.
with AP
