Donald Trump told supporters that his arrest is imminent and issued an extraordinary call for them to protest as a New York grand jury investigates hush money payments to women who alleged sexual encounters with the former president.

Even as Mr. Trump’s lawyer and spokesperson said there had been no communication from prosecutors, he declared in a post on his social media platform that he expects to be taken into custody on Tuesday.

His message seemed designed to preempt a formal announcement from prosecutors and to galvanize outrage from his base of supporters in advance of widely anticipated charges. Within hours, his campaign was sending fundraising solicitations to his supporters, while influential Republicans in Congress and even some declared and potential rival candidates issued statements in his defense.

In a later post that went beyond simply exhorting loyalists to protest about his legal peril, the 2024 presidential candidate directed his overarching ire in all capital letters at the Biden administration and raised the prospect of civil unrest: “IT’S TIME!!!” he wrote. “WE JUST CAN’T ALLOW THIS ANYMORE. THEY’RE KILLING OUR NATION AS WE SIT BACK & WATCH. WE MUST SAVE AMERICA!PROTEST, PROTEST, PROTEST!!!”

The messaging evoked rhetoric he used shortly before the riot at the U.S. Capitol on January 6, 2021. After hearing from the president at a Washington rally that morning, his supporters marched to Capitol Hill and tried to stop the congressional certification of Democratic President Biden’s White House victory, breaking through doors and windows of the building and leaving officers beaten and bloodied.

New York District Attorney Alvin Bragg is thought to be eyeing charges in the hush money investigation, and recently offered Mr. Trump a chance to testify before the grand jury. Local law enforcement officials are bracing for the public safety ramifications of an unprecedented prosecution of a former American president.

In an internal email following Mr. Trump’s statements, Mr. Bragg said law enforcement would ensure that the 1,600 people who work in his office would remain safe, and that “any specific or credible threats” would be investigated.

“We do not tolerate attempts to intimidate our office or threaten the rule of law in New York,” he wrote, and added: “In the meantime, as with all of our investigations, we will continue to apply the law evenly and fairly, and speak publicly only when appropriate.”

There has been no public announcement of any time frame for the grand jury’s secret work in the case. At least one additional witness is expected to testify, further indicating that no vote to indict has yet been taken, according to a person familiar with the investigation.

That did not stop Mr. Trump from taking to his social media platform to say “illegal leaks” from Mr. Bragg’s office indicate that “THE FAR & AWAY LEADING REPUBLICAN CANDIDATE & FORMER PRESIDENT OF THE UNITED STATES OF AMERICA, WILL BE ARRESTED ON TUESDAY OF NEXT WEEK.”

A lawyer for Mr. Trump, Susan Necheles, said his post was “based on the media reports,” and a spokesperson said there had been “no notification” from Mr. Bragg’s office, though the origin of Mr. Trump’s Tuesday reference was unclear. The district attorney’s office declined to comment.

Mr Trump’s aides and legal team have been preparing for the possibility of an indictment. Should that happen, he would be arrested only if he refused to surrender. Mr. Trump’s lawyers have previously said he would follow normal procedure, meaning he would likely agree to surrender at a New York Police Department precinct or directly to Mr. Bragg’s office.

The indictment of Mr. Trump, 76, would be an extraordinary development after years of investigations into his business, political and personal dealings.

Even as Mr. Trump pursues his latest White House campaign — his first rally is set for Waco, Texas, later this month and he shook hands and took selfies with fans during a public appearance Saturday evening at the NCAA Division I wrestling championships in Tulsa, Oklahoma — there is no question an indictment would be a distraction and give fodder to opponents and critics tired of the legal scandals that have long enveloped him.

Besides the hush money inquiry in New York, Mr. Trump faces separate criminal investigations in Atlanta and Washington over his efforts to undo the results of the 2020 election.

A Justice Department special counsel has also been presenting evidence before a grand jury investigating Mr. Trump’s possession of hundreds of classified documents at his Florida estate. It is not clear when those investigations will end or whether they might result in criminal charges, but they will continue regardless of what happens in New York, underscoring the ongoing gravity — and broad geographic scope — of the legal challenges facing the former president.

After his post, Republican House Speaker McCarthy decried any plans to prosecute Mr. Trump as an “outrageous abuse of power by a radical DA” whom he claimed was pursuing “political vengeance.” Elise Stefanik, the third-ranking House Republican, issued a statement with a similar sentiment.

The grand jury has been hearing from witnesses, including former Trump lawyer Michael Cohen, who says he orchestrated payments in 2016 to two women to silence them about sexual encounters they said they had with Mr. Trump a decade earlier.

Mr. Trump denies the encounters occurred, says he did nothing wrong and has cast the investigation as a “witch hunt” by a Democratic prosecutor bent on sabotaging the Republican’s 2024 campaign. Mr. Trump also has labeled Mr. Bragg, who is Black, a “racist” and has accused the prosecutor of letting crime in the city run amok while he has focused on Mr. Trump.

Mr. Bragg’s office has apparently been examining whether any state laws were broken in connection with the payments or the way Mr. Trump’s company compensated Mr. Cohen for his work to keep the women’s allegations quiet.

Porn actor Stormy Daniels and at least two former Trump aides — onetime political adviser Kellyanne Conway and former spokesperson Hope Hicks — are among witnesses who have met with prosecutors in recent weeks.

Mr. Cohen has said that at Trump’s direction, he arranged payments totaling $280,000 to Ms. Daniels and Playboy model Karen McDougal. According to Mr. Cohen, the payouts were to buy their silence about Mr. Trump, who was then in the thick of his first presidential campaign.

Mr. Cohen and federal prosecutors said Mr. Trump’s company paid him $420,000 as reimbursement for the $130,000 payment to Ms. Daniels and to cover bonuses and other supposed expenses. The company classified those payments internally as legal expenses. The $150,000 payment to Ms. McDougal was made by the then-publisher of the supermarket tabloid National Enquirer, which kept her story from coming to light.

Federal prosecutors agreed not to prosecute the Enquirer’s corporate parent in exchange for its cooperation in a campaign finance investigation that led to charges against Mr. Cohen in 2018.

Prosecutors said the payments to Ms. Daniels and Ms. McDougal amounted to impermissible, unrecorded gifts to Mr. Trump’s election effort. Mr. Cohen pleaded guilty, served prison time and was disbarred. Federal prosecutors never charged Trump with any crime.