The attorney general issued an initial four-page letter in March 2019 — two days after receiving the 381-page Mueller report — that purported to summarize its principal conclusions. But within days, Mr. Mueller sent letters to Mr. Barr protesting that he had distorted its findings and asking him to swiftly release the report’s own summaries. Instead, Mr. Barr made the report public only weeks later, after a fuller review to black out sensitive material.

Among the issues Judge Walton flagged: Mr. Barr declared that the special counsel had not found that the Trump campaign had conspired or coordinated with Russia in its efforts to influence the 2016 presidential election, and left it at that.

But while Mr. Mueller did conclude that he found insufficient evidence to charge any Trump associates with conspiring with the Russians, Mr. Barr omitted that the special counsel had identified multiple contacts between Trump campaign officials and people with ties to the Russian government and that the campaign expected to benefit from Moscow’s interference.

Judge Walton also wrote that the special counsel “only concluded” that the investigation did not establish that the contacts rose to “coordination” because Mr. Mueller interpreted that term narrowly, requiring, in the report’s words, agreement that is “more than the two parties taking actions that were informed by or responsive to the other’s actions or interests.”

In addition, Mr. Barr told the public in March that Mr. Mueller had made no decision about whether the president obstructed justice, then pronounced Mr. Trump cleared of those suspicions.

But Mr. Barr “failed to disclose to the American public,” Judge Walton wrote, that Mr. Mueller had explained that it would be inappropriate to make a judgment while the president was still in office about whether he committed obstruction crimes. The report also said that if the evidence had cleared Mr. Trump, Mr. Mueller would have said so, but he was unable to exonerate him.

“The speed by which Attorney General Barr released to the public the summary of Special Counsel Mueller’s principal conclusions, coupled with the fact that Attorney General Barr failed to provide a thorough representation of the findings set forth in the Mueller report, causes the court to question whether Attorney General Barr’s intent was to create a one-sided narrative about the Mueller report — a narrative that is clearly in some respects substantively at odds with the redacted version of the Mueller report,” Judge Walton wrote.