A federal appeals court said on Thursday that it would not block the Justice Department from releasing a report by the special counsel Jack Smith about the two now-closed investigations he conducted into President-elect Donald J. Trump.

In a brief and unsigned order, the U.S. Court of Appeals for the 11th Circuit, in Atlanta, rejected an emergency request from Mr. Trump’s legal team to stop the report from coming out.

The move is part of a complicated back-and-forth fight in the final days before Mr. Trump is set to become president again over whether at least some of Mr. Smith’s report will ever be released. The order does not necessarily mean the report will become public immediately.

Both sections of Mr. Smith’s two-volume report remain for the moment under an injunction put in place this week by a lower-court judge in Florida that is temporarily blocking their release.

The Justice Department has already said that it intends to hold off on releasing the volume that concerns the case in Florida in which Mr. Trump was accused of mishandling classified documents after he left office.

But the department has said that it wants to release the other volume, which details Mr. Smith’s decisions in the case he filed in Washington accusing Mr. Trump of seeking to overturn the 2020 election.

In its order on Thursday night, the appeals court left the injunction in place but said the Justice Department could take further action seeking to appeal it. Later on Thursday, prosecutors appealed that injunction, putting before the appeals court the question of whether to remove it.

Either way, the injunction, which was issued by Judge Aileen M. Cannon, who oversaw the classified documents case, is scheduled to last only another three days.

If it expires on its own or is nullified by the appeals court, Attorney General Merrick B. Garland could go ahead with his plans to release the portion of Mr. Smith’s report concerning the election interference case.

In the meantime, Mr. Trump’s lawyers could try further to stop or delay the release of the report by asking the Supreme Court to step in.

Mr. Smith was forced to drop both criminal cases after Mr. Trump won the 2024 election because of a Justice Department policy that sitting presidents should be seen as temporarily immune from prosecution while in office.

While that meant Mr. Trump had already largely won the legal battle, a final clash has emerged over whether the public will see any of Mr. Smith’s report about his investigative findings and prosecutorial decisions. Department regulations require him to provide that information to Mr. Garland.

The Justice Department has said that Mr. Garland does not intend to release the volume about the classified documents case because charges remain pending against two of Mr. Trump’s co-defendants. Prosecutors have acknowledged that it would not be fair to the men to air the special counsel’s decision-making in the case because it could affect their right to a fair trial.

The new administration is widely seen as being likely to end that case altogether, either by pardoning the co-defendants or by simply dropping it. But it would then be up to Mr. Trump’s appointees whether to release that portion of the report, which Mr. Trump’s legal team has fought to keep suppressed.