“There will be no extension of the TikTok deadline,” Mr Trump said.
The president has given the Chinese owner of the app, ByteDance, 45 days to sell it.
TikTok declined to comment on Mr Trump's statement.
If ByteDance doesn’t sell the app, then US firms will be barred from doing business with it after the deadline has elapsed.
“We’ll see what happens. It’ll either be closed up or they’ll sell it,” said Mr Trump on Thursday, when explaining that the deadline would not be pushed back.
According to Mr Trump, TikTok and other Chinese apps that collect data on US citizens pose a national security threat.
TikTok had previously said it was "shocked" by the prospect of a ban.
It has launched a legal challenge.
ByteDance also faces restrictions on selling its assets to firms outside China, which further complicates the sale of TikTok.
Among the firms known to have expressed interest in buying TikTok are Microsoft and US retail giant Walmart.