A federal appeals court ruled Tuesday against a foreign company embroiled in a secret subpoena fight believed to involve special counsel Robert S. Mueller III’s far-reaching investigation of Russian interference in the 2016 election.

For weeks, the court had kept secret the nature of the fight over evidence, leading to a guessing game about who the secret witness is — a government official, a private citizen or a company.

Officials have not confirmed who the prosecutors on the case are, but on the day the court order under appeal was issued, two lawyers were observed exiting a sealed hearing before Chief Judge Beryl A. Howell of the U.S. District Court for the District of Columbia — who oversees grand-jury proceedings — along with five prosecutors with the special counsel’s office, including appellate specialist Michael Dreeben.

Siding with prosecutors Tuesday, the U.S. Court of Appeals for the District of Columbia Circuit issued a vaguely worded judgment that revealed a few new details but still kept the key facts under seal.

“The grand jury seeks information from a corporation owned by Country A,” the three-page decision said. The company had sought to quash the subpoena by arguing it is immune from such demands under the Foreign Sovereign Immunities Act and because complying with the subpoena would cause the company to violate its own domestic laws.

The appeals court disagreed, saying that in this case, prosecutors have met the burden of having reason to believe the evidence they are seeking relates to an act “outside the territory of the United States” but one that also had “a direct effect in the United States.”

A lower-court judge already had sided with the U.S. prosecutors and against the company, according to the ruling.

“When the corporation failed to produce the requested information, the court held the corporation in contempt, imposing a fixed monetary penalty to increase each day the corporation fails to comply,” the appeals court noted.

The court has not identified the company’s lawyers or the specific prosecutors fighting to enforce the subpoena.

The appeals panel held sealed oral arguments on the matter Friday, during a closed hearing that was so secure that reporters were removed from an entire floor of the courthouse, apparently to prevent them from seeing the attorneys on the case.

In its ruling, the appeals court was particularly dismissive of the claims that the unidentified country’s domestic laws barred compliance with the subpoena.

“The corporation has fallen well short” of meeting the legal requirement for such a claim, the court wrote. “The text of the foreign law provision the corporation relies on does not support its position,” and statements from one of the country’s regulators and the company’s own lawyer “lack critical indicia of reliability,” the ruling said.

For that reason, the appeals court concluded, “we are unconvinced that Country A’s law truly prohibits the corporation from complying with the subpoena.”

The framing of the debate suggests that whatever the company is, it is not one that has a significant business presence in the United States, because foreign firms operating in America typically comply with demands from U.S. authorities for evidence.

It was not immediately clear if the unidentified company might try to appeal the decision to the Supreme Court. Lawyers for the firm could not be identified.

Spencer S. Hsu contributed to this report.