The Biden administration has decided to fight to keep secret most of a Trump-era Justice Department memo related to former Attorney General William P. Barr’s much-disputed declaration in 2019 clearing President Donald J. Trump of illegally obstructing justice in the Russia investigation.

In a late-night filing Monday, the Justice Department appealed part of a district-court ruling that ordered it to make public the entire memo. It was written at the same time that Mr. Barr sent a letter to Congress claiming the evidence in the then-still secret report by the special counsel, Robert S. Mueller III, was insufficient to charge Mr. Trump with a crime.

The Justice Department did release the first page and a half of the nine-page memo. While Mr. Mueller had declined to render a judgment about what the evidence added up to because the department’s policy was not to charge a sitting president, the memo said Mr. Barr was justified in making a decision in order to shape public understanding of the report.

“Although the special counsel recognized the unfairness of levying an accusation against the president without bringing criminal charges, the report’s failure to take a position on the matters described therein might be read to imply such an accusation if the confidential report were released to the public,” wrote Steven A. Engel and Edward C. O’Callaghan, two senior Trump-era Justice Department officials.

The Mueller report itself — which Mr. Barr permitted to become public weeks after his letter to Congress had created an impression that the fruits of Mr. Mueller’s inquiry cleared Mr. Trump of obstruction — detailed multiple actions by Mr. Trump that many legal specialists say were clearly sufficient to ask a grand jury to consider indicting him for obstruction of justice.

Those actions included attempting to bully his White House counsel, Donald F. McGahn II, into falsifying a record to cover up an earlier attempt by Mr. Trump to fire Mr. Mueller, and dangling a potential pardon at Mr. Trump’s former campaign chairman, Paul Manafort, to encourage him not to cooperate with investigators.

The new Justice Department filing also apologized for and defended its Barr-era court filings about the memo, which Judge Amy Berman Jackson had labeled “disingenuous,” saying that they could have been written more clearly but were nevertheless accurate.

“The government acknowledges that its briefs could have been clearer, and it deeply regrets the confusion that caused,” the Justice Department said. “But the government’s counsel and declarants did not intend to mislead the court, and the government respectfully submits” that any missteps still did not warrant releasing the entire memo.

Mr. Barr’s claim — which he made weeks before releasing the Mueller public — that the evidence gathered showed that Mr. Trump did not commit a chargeable offense of obstruction has been widely criticized as deeply misleading.

Among other fallout, a government watchdog group, CREW, filed a Freedom of Information Act lawsuit in the United States District Court in Washington seeking disclosure of an internal memo about the matter.

Earlier this month, Judge Jackson issued a scathing ruling in that case saying that the Barr-era Justice Department had been “disingenuous to this court” about the nature of the memo in court filings by arguing that it could be lawfully kept secret under an exemption for pre-decisional deliberations. She wrote that she had made the discovery after insisting that she read it herself.

While the Barr-era Justice Department told her the memo concerned deliberations about whether Mr. Trump should be charged with obstruction, the memo itself showed that Mr. Barr had already decided not to do so, and the memo was instead about strategy and arguments that could be mustered to quash the idea. She ordered the entire document released.

The Biden-era Justice Department had until Monday to respond. In its filing, it acknowledged that its earlier filings “could have been clearer, and it deeply regrets the confusion that caused.” But it also insisted that its “declarations and briefs were accurate and submitted in good faith.”

The decision that Mr. Barr was actually making, the department said, was about whether to decide whether the evidence was sufficient to charge Mr. Trump someday — not whether he should be charged at that moment, since longstanding department legal policy is to consider sitting presidents temporarily immune from prosecution while they are in office.

And, it said, the legal analysis in the second part of the memo — the portion it is appealing to keep secret — was, in fact, pre-decisional, even though the memo was completed after Mr. Barr made his decision, because it memorialized legal advice that department lawyers had previously provided to the attorney general.