TikTok and ByteDance say an injunction is also justified because Donald Trump is about to replace Joe Biden as president.
Trump has previously indicated he would overturn the law.
“The public interest favours providing sufficient time for the Supreme Court to conduct an orderly review process, and for the incoming Administration to evaluate this exceptionally important case,” ByteDance and TikTok said in their emergency legal filing.
They added that even a temporary ban from early 2025 would have “devastating effects” on its operations.
It would be “inflicting irreparable injury by silencing Petitioners and the 170 million Americans who use the platform each month,” the filing added.
The company also said that even a temporary ban could cause a loss of revenue, as well as a loss of users and creators who make content for the platform.
On Friday, judges rejected the idea that the law was unconstitutional – saying it was the result of “extensive, bipartisan action” by lawmakers.
They further concluded the law was “carefully crafted to deal only with control by a foreign adversary, and it was part of a broader effort to counter a well-substantiated national security threat posed by the PRC (People’s Republic of China).”