Former President Donald J. Trump has been informed that he could soon face federal indictment for his efforts to hold onto power after his 2020 election loss, potentially adding to the remarkable array of criminal charges and other legal troubles facing him even as he campaigns to return to the White House.

Mr. Trump was informed by his lawyers on Sunday that he had received a so-called target letter from Jack Smith, the special counsel investigating his attempts to reverse his defeat at the polls, Mr. Trump and other people familiar with the matter said on Tuesday. Prosecutors use target letters to tell potential defendants that investigators have evidence tying them to crimes and that they could be subject to indictment.

“Deranged Jack Smith” sent Mr. Trump a letter on Sunday night informing him he was a “TARGET of the January 6th Grand Jury” investigation, Mr. Trump said in a post on his social media platform.

Such a letter “almost always means an Arrest and Indictment,” wrote Mr. Trump, whose campaign is rooted in accusations of political persecution and a promise to purge the Justice Department and Federal Bureau of Investigation of personnel he sees as hostile to him and his agenda.

Mr. Smith’s spokesman had no comment.

An indictment of Mr. Trump would be the second brought by Mr. Smith, who is also prosecuting the former president for risking national security secrets by taking classified documents from the White House and for obstructing the government’s efforts to reclaim the material.

Mr. Trump is also under indictment in Manhattan on charges related to hush money payments to a porn star before the 2016 election. And he faces the likelihood of charges from the district attorney in Fulton County, Ga., who has been conducting a wide-ranging inquiry into Mr. Trump’s attempts to reverse his 2020 election loss in that state.

It is not clear what specific charges Mr. Smith and his prosecutors might be considering, but they appear to have assembled evidence about an array of tactics that Mr. Trump and his allies used to try to stave off his election defeat.

Those efforts included assembling slates of so-called fake electors from swing states that Mr. Trump lost; pressuring state officials to block or delay Joseph R. Biden Jr.’s victories; seeking to persuade Vice President Mike Pence to impede congressional certification of the Electoral College outcome; raising money based on false claims of election fraud; and rallying supporters to come to Washington and march on the Capitol on Jan. 6, 2021.

It also remains unknown whether others might be charged along with Mr. Trump. Several of his closest allies during his efforts to remain in office, including Rudolph W. Giuliani, who was serving as his personal lawyer, and John Eastman, who promoted the idea that Mr. Pence could keep Congress from certifying Mr. Biden’s victory, said through their lawyers that they had not received target letters.

Just hours after Mr. Trump disclosed his receipt of the target letter, the Michigan attorney general announced felony state charges against 16 people for their involvement in an attempt to overturn Mr. Biden’s victory in the state by convening a slate of pro-Trump electors.

The news of another potential indictment of Mr. Trump underscored the stakes of an intensifying legal and political battle whose consequences are both incalculable and unpredictable.

Mr. Trump remains a dominant front-runner for the Republican presidential nomination, in spite of — or to some degree because of — the growing list of charges and potential charges against him.

His campaign strategy has been to embrace the investigations as evidence of a plot by a Democratic administration to deny him and his supporters a victory in 2024, a message that continues to resonate among his followers. He was raising money off news of the target letter within hours of disclosing that he had received it.

But for Mr. Trump, the stakes are deeply personal, given the serious threat that he could face prison time if convicted in one or more of the cases. In that sense, a winning campaign — and the power to make at least the federal cases go away by pardoning himself or directing his Justice Department to dismiss them — is also a battle for his liberty.

Mr. Trump spent much of Tuesday promoting a scorched-earth political strategy, consulting with allies in Washington including Speaker Kevin McCarthy and Representative Elise Stefanik, a New York Republican and onetime critic who has become one of his staunchest defenders. Mr. Trump urged Ms. Stefanik to go “on offense” during a lengthy call from his golf club in Bedminster, N.J., according to a person with knowledge of the conversation.

His main rival at the moment for the Republican nomination, Gov. Ron DeSantis of Florida, said Mr. Trump was a victim of the “politicization” of the Justice Department, continuing a pattern in which prominent figures in his party remain leery of criticizing him and drawing the ire of his supporters.

At least two grand juries in Washington have been hearing matters related to Mr. Trump’s efforts to stay in office. A trial, if it comes to that, would likely be held in Federal District Court in Washington, where many of the Jan. 6 rioters and leaders of two far-right groups, the Proud Boys and the Oath Keepers, have been prosecuted.

Based on the outcomes of those trials, the jury pool in Washington would likely be less favorable to the former president than the one that would be empaneled from a largely pro-Trump region around Fort Pierce, Fla., where the classified documents trial is currently scheduled to take place.

Two of Mr. Trump’s lawyers, Todd Blanche and Christopher M. Kise, briefly mentioned the new target letter at a pretrial hearing in Florida on Tuesday on the documents case. While Mr. Kise and Mr. Blanche gave no details about what the letter said, they used it to argue that Mr. Trump was essentially being besieged by prosecutors and that the trial in the classified documents case should be delayed until after the 2024 election.

In disclosing that he had received the target letter, Mr. Trump said he was given four days to testify before a grand jury if he chooses. He is expected to decline. The timetable suggested by the letter suggests that he will not be charged this week, according to people familiar with the situation.

Fani T. Willis, the district attorney in Fulton County, Ga., who has pressed ahead with her own investigation of Mr. Trump and his allies, could bring charges as early as next month. If she were to proceed first, that could complicate Mr. Smith’s case. Accounts of witnesses called to testify both cases could vary slightly, seeding doubts about their testimony, for instance — which might explain why Mr. Smith is moving fast, according to former federal prosecutors.

Federal investigators were slow to begin investigating all the efforts to overturn the results of the 2020 election, overwhelmed with prosecuting the hundreds of rioters who illegally entered the Capitol. The initial plan for investigating the attack’s planners, drafted by the Trump-appointed U.S. attorney in Washington and later adopted by Attorney General Merrick B. Garland, did not include any explicit reference to the former president. The F.B.I. took a similar tack.

However, in the months leading up to Mr. Smith’s appointment as a special counsel last fall, there were strong indications that federal prosecutors were pivoting to examine whether Mr. Trump and his allies may have committed crimes.

The F.B.I.’s Washington field office opened an investigation in April 2022 into electors who pledged fealty to Mr. Trump in states he had lost. Earlier, the authorities had seized the cellphones of Mr. Eastman, a legal architect of Mr. Trump’s efforts to overturn his 2020 election loss, and Jeffrey Clark, a lawyer whom Mr. Trump had tried to install as the acting attorney general.

Among the crimes that prosecutors and agents intended to investigate were mail and wire fraud, conspiracy and obstruction of an official proceeding before Congress.

By late last year, the various investigations were brought under Mr. Smith, who moved quickly with a flurry of activity, including subpoenas and witness interviews.

Mr. Smith and his team do not appear to be done. A spokesman for former Gov. Doug Ducey of Arizona said that Mr. Smith’s team reached out to him after The Washington Post reported that Mr. Trump had tasked Mr. Pence with pressuring Mr. Ducey to overturn Mr. Biden’s narrow victory there.

The spokesman said that Mr. Ducey will do “the right thing” and that he had done so since the election. It was unclear whether the contact was to request a voluntary interview by Mr. Ducey or a grand jury appearance.

Mr. Trump’s son-in-law, Jared Kushner, appeared before one of the grand juries in June, according to people familiar with his appearance. Mr. Giuliani had a recent interview with prosecutors.

Ben Protess, Jonathan Swan and Luke Broadwater contributed reporting.