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A federal judge in Manhattan disclosed on Wednesday that prosecutors have concluded their investigation into campaign finance violations involving President Trump and ordered that they publicly release some of their files, a new twist in a case that had threatened to upend the Trump presidency.

The judge’s order did not answer one of the lingering questions of the investigation: whether prosecutors in the United States attorney’s office in Manhattan still plan to file additional charges in connection with the case.

The investigation, which centered on hush money payments arranged during the 2016 presidential campaign to two women who said they had affairs with Mr. Trump, already resulted in the conviction of the president’s former fixer, Michael D. Cohen.

Mr. Cohen, who is now serving a three-year prison sentence, has said he helped arrange the hush money at the direction of Mr. Trump, an accusation that the federal prosecutors in Manhattan ultimately repeated in court papers.