Trump on Friday said he would ban the app, which is especially popular with young audiences who create and watch its short-form videos.
His threat has caused great concern for US TikTok users, particularly content creators who make money on the platform.
Similarly, Treasury Secretary Steven Mnuchin said Sunday on ABC that TikTok should be sold or blocked in the US.
Microsoft announced Sunday it would continue talks to acquire the US operations of popular video-sharing app TikTok, after meeting with President Donald Trump who was seemingly backing off his earlier threats to ban the Chinese-owned platform.
"Following a conversation between Microsoft CEO Satya Nadella and President Donald J Trump, Microsoft is prepared to continue discussions to explore a purchase of TikTok in the United States," the company said in a statement, acknowledging the "importance of addressing the President's concerns" over national security.