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The company said it was "shocked" by an executive order from the US President outlining the ban, reports BBC.
TikTok said it would "pursue all remedies available" to "ensure the rule of law is not discarded".
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."
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 Trump.
The Trump administration claims that the Chinese government has access to user information gathered by TikTok, which the company has denied.
"We have made clear that TikTok has never shared user data with the Chinese government, nor censored content at its request," TikTok 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.