The video app, which is owned by the Chinese company ByteDance, has an estimated 65-80 million active monthly users in the U.S., who share 15-second videos with quick edits, music, and filters.
TikTok has exploded in the last year, with over 175 million downloads in the U.S. and over 1 billion users worldwide.
But since last fall, U.S. lawmakers have been calling for an investigation of TikTok's relationship with its parent company and the Chinese government and of whether those reported ties pose a counterintelligence threat in America.
Pompeo told Fox News the Trump administration is "certainly looking" at banning Chinese social media apps, including TikTok.
In response, a TikTok spokesperson told ABC News Tuesday the company is "led by an American CEO, with hundreds of employees and key leaders across safety, security, product, and public policy here in the U.S. We have no higher priority than promoting a safe and secure app experience for our users."
Pompeo cast TikTok as a security threat, accusing it of sharing users' data with the Chinese government. When asked by Fox's Laura Ingraham Monday night if he would recommend that people download the app, he responded, "Only if you want your private information in the hands of the Chinese Communist Party."
But the TikTok spokesperson denied that was true: "We have never provided user data to the Chinese government, nor would we do so if asked."
The company is owned by ByteDance, a Chinese tech firm that also started travel search and real estate search sites and is considered one of the world's most valuable start-ups.
TikTok has tried to distance itself from ByteDance, saying on its website that it "does business through subsidiaries of ByteDance Ltd., which is backed by global institutional investors."
It also announced Monday it would remove the app from Hong Kong because of the Chinese government's new national security law, which gives Beijing tighter control of the territory that was supposed to be semi-autonomous, including requiring tech companies there to hand over user data if requested.
But Pompeo has cast virtually all Chinese companies as a security threat because of the Chinese internet security law, which allows the government to request access to their data. He did not provide specific evidence Monday that the Chinese government has requested that information from TikTok.
The State Department declined to provide more details. An official from the Office of the Director of National Intelligence declined to comment specifically on whether there is any intelligence assessment on TikTok.
But the official told ABC News, "Every Chinese technology company is required by Chinese law to provide information they obtain, or information stored on their networks, to Chinese authorities if requested to do so. All Americans should be concerned that their images, biometrics, locational and other data stored on Chinese apps must be turned over to China's state security apparatus upon request."
Several U.S. agencies and branches of the military have already banned TikTok's use for their personnel, including the Transportation Security Administration and the U.S. Army.
TikTok has become enormously popular amid coronavirus shutdowns across the U.S., with users spending an estimated 52 minutes each day and the number of unique visitors growing exponentially between January and April, according to Wallaroo Media, a digital advertising firm.
Videos automatically play one after the other, ranging from attempts at viral dance moves to the comedian Sarah Cooper's mocking lip-sync performances as President Donald Trump, which have earned her over 3 million likes. Cooper's PR did not respond to questions about the administration's possible ban.
Last week, India banned the app amid growing tensions with China over a disputed border area high in the Himalaya mountains, casting it and 58 other Chinese-owned apps as security concerns that the Chinese government could exploit.
Australian officials have also said they are considering a ban.
ABC News' Karson Yiu and Catherine Thorbecke contributed to this report.
This report was featured in the Wednesday, July 8, 2020, episode of “Start Here,” ABC News’ daily news podcast.
"Start Here" offers a straightforward look at the day's top stories in 20 minutes. Listen for free every weekday on Apple Podcasts, Google Podcasts, Spotify, the ABC News app or wherever you get your podcasts.