The Supreme Court on Tuesday allowed hefty contempt fines to resume against a mysterious foreign-owned company that is locked in a battle over evidence with federal prosecutors believed to be working for special counsel Robert Mueller.

But the unidentified firm is continuing its broader fight to avoid having to comply with a subpoena issued by a grand jury suspected of working in conjunction with Mueller's ongoing probes.

Now it will face a daily fine of $50,000 as that fight continues, the D.C. Circuit revealed in an opinion published later Tuesday.

Last month, in response to a request by the company, Chief Justice John Roberts issued a stay on the fines the firm faced for not complying with that subpoena.

On Tuesday, in a filing that did not note a dissent from any justice, the Supreme Court effectively lifted Roberts' stay of the fines, which he had imposed over the holidays until the full court could review the matter. Tuesday's order suggests at least five justices opposed a stay.

Separately, the company has asked the Supreme Court for permission to file an application for the high court to hear its challenge to the subpoena. The court has yet to rule on that request, and may not anytime soon, according to legal experts.

"The reality is that the court declining to issue a stay suggests to me that they are not going to be in any hurry to expedite the petition," said Steve Vladeck, a national security lawyer and professor at the University of Texas School of Law.

The company in August filed a legal action seeking to quash the subpoena, which was issued by a grand jury sitting in U.S. District Court in Washington, D.C. That lawsuit is sealed from public view.

Judge Beryl Howell rejected the request and imposed escalating fines after finding that the company was in contempt for refusing to comply with the subpoena, court records show.

The company then appealed her decision to the federal appeals court in Washington.

The company, according to court records, argued it was immune from the subpoena under the Foreign Sovereign Immunities Act. The firm also argued that the subpoena was "unreasonable and oppressive" under federal criminal procedure rules because it would require the company to violate the law of the country that owns it.

The suspicion that the subpoena was issued by a grand jury working with Mueller stems from the fact that a Politico reporter overheard a man in October ask an appeals court clerk asked for a copy of "the special counsel's latest sealed filing so that the man's law firm could craft its response," Politico has reported. That request came on the same day that a filing in the subpoena-related appeals case was due.

"Three hours later, a sealed response in the grand-jury dispute was submitted to the D.C. Circuit," Politico reported.

Mueller is investigating Russian interference in the 2016 presidential election, possible collusion in that meddling by members of Donald Trump's campaign and possible obstruction of justice by President Trump himself. Trump has denied any wrongdoing.

CNN reported that its reporters in September saw several prosecutors from Mueller's office enter Howell's courtroom shortly after she issued a ruling upholding the subpoena. The same prosecutors were spotted entering Howell's court Oct. 5, after the appeals court referred the case back to her for a hearing.

On Dec. 14, the appeals court heard arguments over the company's request to quash the subpoena, without the public being allowed to attend the hearing. Before arguments began, the entire floor containing the courtroom was closed to the public.

On Dec. 18, a three-judge appeals panel rejected each of the claims raised by the company. Four days later, the company asked the Supreme Court to stay the contempt fines.

Experts say that Tuesday's order refusing to stay the fines, will not end the matter. But it is a setback for the company, particularly given the absence of any noted dissents in the order.

"If I am their lawyers, I am not optimistic, given that there were no recorded dissents," Vladeck said. "So I think that the question is whether the mystery corporation is willing to keep paying the contempt fine while it presses the court to take the question on the merits."