Three years after a mob of his supporters stormed the Capitol, former President Donald J. Trump will make his latest and potentially most consequential argument in the coming week for why he should not be held responsible for seeking to overturn the 2020 election.

Impeachment proceedings, the House Jan. 6 committee’s inquiry and two separate criminal investigations have established a comprehensive set of facts about Mr. Trump’s deep involvement in overlapping efforts to remain in office despite having been defeated at the polls.

But when — or even whether — he will ultimately face a trial on charges related to those efforts remains unclear. One of the most decisive factors in getting an answer to those questions will be the success or failure of the arguments his legal team plans to make on Tuesday in a federal appeals court in Washington.

Mr. Trump’s lawyers are banking on a long shot, hoping to convince a three-judge panel of the U.S. Court of Appeals for the District of Columbia Circuit that the Constitution affords him complete immunity from actions he undertook as president. The assertion, while untested in the courts, has the advantage to the former president of chewing up time in the service of his strategy of trying to delay any trial until after Election Day.

Should Mr. Trump be elected, he could seek to order the federal charges against him to be dropped. The pace and outcome of the appellate challenges stemming from his immunity claim could also affect the timing of the three other criminal cases he is facing.

The legal maneuvering is playing out against a backdrop in which President Biden is casting the 2024 campaign as a test of whether democratic norms and institutions can hold against Mr. Trump and his push to convince voters that he is not a perpetrator of the chaos of Jan. 6 but a victim of an effort to silence him and his supporters.

Mr. Trump has been making plans to attend the appeals court hearing even though he is not required to be there, a further indication of how central fighting his prosecutions has become to his political strategy heading into the Republican primary campaign.

When Mr. Trump was impeached for inciting the events of Jan. 6, 2021, his defenses were that the First Amendment protected his baseless claims of voter fraud, the House had rushed its inquiry and the Senate could not convict him because he was out of office by the time it held a trial.

But his plan to the tell the three appellate judges in the federal courthouse three blocks from the Capitol that he is immune from prosecution raises broader constitutional issues.

Because no former president has ever been prosecuted before — just as no president before Mr. Trump ever tried to stay in power after losing an election — there are few definitive precedents to guide judges in considering his immunity defense.

His immunity claim has already bounced around various courts for nearly three months, forcing the trial judge to put the larger case on hold until the issue is resolved. The question is likely to end up at the Supreme Court, but even if the justices eventually reject an immunity defense, the time consumed by the arguments could help run down the clock enough to keep the case from going to trial before this fall’s election.

In court filings, Mr. Trump’s legal team has contended that the Constitution gives courts no jurisdiction to review the official acts of presidents unless Congress has already impeached and convicted them for the same behavior.

His lawyers have also claimed that all of the steps that Mr. Trump took to reverse the election results were exercises of his powers and responsibilities as president, undertaken to protect the integrity of the vote against the possibility of fraud as he saw it.

The prosecution team led by the special counsel, Jack Smith, disagrees. It has argued that former presidents are not immune from being prosecuted for criminally abusing their official powers and that impeachment is irrelevant to issues of criminal law.

In any event, they assert that Mr. Trump was knowingly spreading lies about fraud and was acting in his private role as a candidate seeking to win re-election, not as part of his formal duties as president.

Judge Tanya S. Chutkan, who is handling the case at the trial level in Federal District Court in Washington, rejected Mr. Trump’s immunity claim in December. She ruled that “former presidents do not possess absolute federal criminal immunity for any acts committed while in office.”

Because that flat conclusion rendered irrelevant the distinction between private and official acts, she did not delve into how to think through whether Mr. Trump was acting as the president or as a candidate in his postelection conduct. But Mr. Trump has raised that question again as part of challenging her decision before the federal appeals court.

Once the appeal was filed, Judge Chutkan paused all of the proceedings in the case, imperiling the scheduled March 4 start date for the trial. Concerned that a protracted challenge could significantly delay the trial, Mr. Smith sought to bypass the appeals court altogether and go directly to the Supreme Court.

But the justices rejected his request, sending the issue back to the three-judge panel that is now hearing the case. The panel will consider not just the question of immunity, but others adjacent to it, including an argument that Mr. Trump’s appeal is premature and the immunity issue should only be considered if he is convicted at trial.

The panel includes Judge Karen L. Henderson, a Republican appointee who has sometimes — but not always — voted in ways favorable to Mr. Trump in other politically charged cases. It also includes two Democratic appointees, Judges J. Michelle Childs and Florence Y. Pan, who have not been on the court long enough to have played major roles in previous Trump-related cases.

There are no direct precedents on the broad question of whether presidents have criminal immunity for their official actions.

The Supreme Court has held that presidents are absolutely immune from civil lawsuits related to their official acts, in part to protect them against ceaseless harassment and judicial scrutiny of their day-to-day decisions. The court has also held that presidents can be sued over their personal actions.

The Supreme Court has further found that while presidents are sometimes immune from judicial subpoenas requesting internal executive branch information, that privilege is not absolute. Even presidents, the court has decided, can be forced to obey a subpoena in a criminal case if the need for information is great enough.

But until Mr. Trump wound up in court, the Supreme Court has never had a reason to decide whether former presidents are protected from being prosecuted for official actions. The Justice Department has long maintained that sitting presidents are temporarily immune from prosecution because criminal charges would distract them from their constitutional functions. But since Mr. Trump is not in office, that is not an issue.

The closest the country has come to the prosecution of a former president over official actions came in 1974, when Richard M. Nixon resigned to avoid being impeached over the Watergate scandal. But a pardon by his successor, President Gerald Ford, protected Nixon from indictment by the Watergate special prosecutor.

Mr. Smith’s team has argued that Ford’s pardon — and Nixon’s acceptance of it — demonstrates that both understood that Nixon was not already immune. Mr. Trump’s team has sought to counter that point by arguing — inaccurately — that Nixon only faced potential criminal charges over private actions, like tax fraud. But the special prosecutor weighed charging Nixon with abusing his office to obstruct justice.

Mr. Trump’s team has argued that denying his claims risks unleashing a routine practice of prosecuting former presidents for partisan reasons. But Mr. Smith’s team has argued that if courts endorse Mr. Trump’s theory, then future presidents who are confident of surviving impeachment could, with impunity, commit any number of crimes in connection with their official actions.

“Such a result would severely undermine the compelling public interest in the rule of law and criminal accountability,” prosecutors wrote.

If judges and justices want to dispose of the dispute without definitively ruling on whether presidents are immune from prosecution for official acts, they could do so by holding that the specific steps Mr. Trump took to remain in office and that are charged in the federal indictment were not official actions. If so, the broader immunity question would not matter and the prosecution could proceed.

The acts by Mr. Trump cited in the indictment include using deceit to organize fake slates of electors and to try to get state officials to subvert legitimate election results; trying to get the Justice Department and Vice President Mike Pence to help fraudulently alter the results; directing his supporters to the Capitol on Jan. 6, 2021, and exploiting the violence and chaos of their ensuing riot.

In their court filings, Mr. Trump’s team has sought to reframe those accusations not only as official actions, but innocuous or even admirable ones.

“All five types of conduct alleged in the indictment constitute official acts,” they wrote. “They all reflect President Trump’s efforts and duties, squarely as chief executive of the United States, to advocate for and defend the integrity of the federal election, in accord with his view that it was tainted by fraud and irregularity.”

Mr. Smith’s team has argued that they should be seen as the efforts of a person seeking office, not of an office holder carrying out government responsibilities.

“Those alleged acts were carried out by and on behalf of the defendant in his capacity as a candidate, and the extensive involvement of private attorneys and campaign staff in procuring the fraudulent slates as alleged in the indictment underscores that those activities were not within the outer perimeter of the office of the presidency,” they wrote.

Judge Chutkan issued her ruling rejecting Mr. Trump’s immunity claim without any detailed analysis of whether his acts were “official.”

If the D.C. Circuit panel on Tuesday — or, later, the full appeals court or the Supreme Court — were to send the matter back to her to take a stab at answering that question before restarting the appeals process, Mr. Trump will, at a minimum, have used up additional valuable time.

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