The company said it was “shocked” by an executive order from the US President outlining the ban.
TikTok said it would “pursue all remedies available” to “ensure the rule of law is not discarded”.
Mr Trump issued a similar order against China’s WeChat in a major escalation in Washington’s stand-off with Beijing.
WeChat’s owner, Tencent, said: “We are reviewing the executive order to get a full understanding.”
As well as WeChat, Tencent is also a leading gaming company and its investments include a 40% stake in Epic Games – the company behind the hugely popular Fortnite video game.
The president has already threatened to ban TikTok in the US, citing national security concerns, and the company is now in talks to sell its American business to Microsoft. They have until 15 September to reach a deal – a deadline set by Mr Trump.
The Trump administration claims that the Chinese government has access to user information gathered by TikTok, which the company has denied.
TikTok, which is owned by China’s ByteDance, said it had attempted to engage with the US government for nearly a year “in good faith”.
However, it said: “What we encountered instead was that the administration paid no attention to facts, dictated terms of an agreement without going through standard legal processes, and tried to insert itself into negotiations between private businesses.”
The executive orders against the short-video sharing platform and the messaging service WeChat are the latest measure in an increasingly broad Trump administration campaign against China.
On Thursday, Washington announced recommendations that Chinese firms listed on US stock markets should be delisted unless they provided regulators with access to their audited accounts.
What did Donald Trump say?
In both executive orders, Mr Trump says that the spread in the US of mobile apps developed and owned by Chinese firms “threaten the national security, foreign policy, and economy of the United States”.
The US government says TikTok and WeChat “capture vast swaths of information from its users”.
“This data collection threatens to allow the Chinese Communist Party access to Americans’ personal and proprietary information.”
The executive order also claims both apps gather data on Chinese nationals visiting the US, allowing Beijing “to keep tabs” on them.
Mr Trump’s executive order also says TikTok’s data collection could allow China to track US government employees and gather personal information for blackmail, or to carry out corporate espionage.
He notes that reports indicate TikTok censors content deemed politically sensitive, such as protests in Hong Kong and China’s treatment of the Uighurs, a Muslim minority.
The orders have been issued under legal authority from the National Emergencies Act and the International Emergency Economic Powers Act.
What does TikTok say?
In its most robust response so far to the US government, TikTok says the executive order that has been issued is based on “unnamed reports with no citations”.
“We have made clear that TikTok has never shared user data with the Chinese government, nor censored content at its request,” it said.
“We even expressed our willingness to pursue a full sale of the US business to an American company.”
Mr Trump said this week he would support the sale to Microsoft as long as the US government received a “substantial portion” of the sale price.
TikTok said the new executive order “risks undermining global businesses’ trust in the United States’ commitment to the rule of law”, adding it sets “a dangerous precedent for the concept of free expression and open markets”.
“We will pursue all remedies available to us in order to ensure that the rule of law is not discarded and that our company and our users are treated fairly – if not by the administration, then by the US courts,” it said.
WeChat ban puts US-China personal ties in peril
Zhaoyin Feng, BBC News Chinese, Washington DC
The TikTok ban is hardly a surprise, as the app has faced scrutiny in the US for months. But the almost identical ban on WeChat is more of a bombshell.
Immediately after President Trump’s executive order was announced, I received a flood of messages on my WeChat. Friends in America and their loved ones in China were in an absolute panic.
They are thousands of miles apart but asking the same question: How are we supposed to keep in touch after WeChat is banned in the US?
It’s nearly impossible to avoid WeChat for those who have any connections to China.
The billion-user app is like WhatsApp, Facebook, Instagram, PayPal, Uber, and even Tinder, all in one ecosystem.
America’s move to block WeChat, a prominent example of China’s tech innovation, will be seen as an attack on its culture, its people and the state. It’ll enhance the popular view in China that Washington is unreasonably suppressing its biggest competitor in technology.
If the ban is fully enforced, it’d be a disaster for anyone who has families, friends or a business in China.
While tit-for-tat has become the new normal in US-China relations, this move will cut off virtually all people-to-people communication between the world’s two most influential countries.
What is the background?
Mr Trump has been waging a trade war against China since taking office.
The US government took action last year against two Chinese communications companies, Huawei and ZTE, including locking them out of government contracts.
Most recently, he has blamed the country for the global coronavirus pandemic, which has crippled the US economy.
Meanwhile, many of the biggest US platforms – Google, Twitter and Facebook – are banned inside China.
TikTok – which has up to 80 million active monthly users in the US – has exploded in popularity in recent years, mostly with people under 20.
The app is reported to have around 800 million active monthly users, with its biggest markets having grown in the US and India.
India has, however, already blocked TikTok, as well as other Chinese apps.
Australia, which has already banned Huawei and ZTE, is also considering banning TikTok.
WeChat is very popular among those users who have connections to China, where major social networking platforms – such as WhatsApp and Facebook – are blocked.
It is also viewed as being a key instrument in China’s internal surveillance apparatus – requiring local users who have been accused of spreading malicious rumours to register a facial scan and voice print.
A seminar held earlier this year by the Australian Strategic Policy Institute think tank discussed how groups within the app would be used to recommend holiday destinations, restaurants and the like on a day-to-day basis, but then switch to spreading political messages in line with Beijing’s thinking at critical times.