The Supreme Court on Tuesday allowed redacted and sealed court documents to be filed by a mysterious foreign government-owned company that wants to avoid being forced to turn over information in an investigation that is widely thought to be led by special counsel Robert Mueller.

The high court did not rule on the merits of the company's argument that it should not have to comply with a subpoena issued by a federal grand jury in Washington earlier this year. That grand jury is believed to be acting at Mueller's request.

Instead, the Supreme Court said it would allow the company's application for a stay in the subpoena, as well as for any responses to be filed without the public seeing all or some of the documents.

The company's petition to the Supreme Court asking for it to consider its appeal of the subpoena was released shortly after the court's order.

Several areas of the filing are blacked out, including the names of the attorneys representing the company, and the "corporate disclosure statement."

But in an unsealed portion, lawyers for the firm that that the Supreme Court "should reverse" a federal appeals court ruling upholding the subpoena "before it upsets foreign relations in a way that an American judicial decision never should."

"The questions presented in this petition go to the very nature of sovereign dignity and power," they said.

The lawyers said the appeals court ruling was the first "in American history to exercise criminal jurisdiction over a foreign state."

"Since America's founding, foreign states have been immune from American criminal jurisdiction, and yet the United States is not overrun with criminal syndicates backed by foreign states," the lawyers argued.

The Supreme Court's decision sets up the possibility that the company will seek to have the case heard by the court's nine justices in a courtroom sealed to the public.

That would be a highly unusual — and possibly unprecedented — event if the Supreme Court granted the company's request for a sealed hearing.

However, the high court could also end up rejecting the company's request that it consider the appeal.

Walter Dellinger, a former acting solicitor general for the United States, told CNBC last week that he was unaware of any past case in which the Supreme Court had allowed a party in a case to file documents asking it to consider a case under seal, or one in which the justices heard oral arguments in a session closed to the public.

The company is currently subject to a $50,000 per day penalty for not complying with the subpoena. The firm's filing at the Supreme Court says federal prosecutors originally asked for contempt fines of $10,000 per day to be imposed, but that a district judge quintupled that amount.

The firm already is on the hook for more than $600,000 in fines after the U.S. Court of Appeals for the Federal Circuit in Washington denied its bid to quash the subpoena.

In its filing partially unsealed Tuesday, the company says federal law did not authorize contempt sanctions, like the one imposed on it in this case, "against a foreign state.