A New York grand jury investigating President Trump over an alleged hush money payment to a porn star appears poised to complete its work soon as law enforcement officials make preparations for possible unrest in the event of an indictment.

Mr. Trump over the weekend claimed without any evidence that he would be arrested on Tuesday, with his representatives later saying he was citing media reports and leaks. 

There was no indication that prediction would come true, though the grand jury appeared to take an important step forward by hearing Monday from a witness favorable to Mr. Trump, presumably so prosecutors could ensure the panel had a chance to consider any testimony that could be seen as exculpatory.

The next steps in a grand jury process shrouded in secrecy remained unclear, and it was uncertain if additional witnesses might be summoned. Yet a city mindful of the riot by Mr. Trump’s loyalists at the Capitol more than two years ago took steps to gird itself from any violence that could accompany the unprecedented prosecution of a former president, while fellow Republicans eyeing the 2024 presidential nomination sized up how an indictment might upend the race.

The testimony from a lawyer with close ties to numerous key Trump aides, Robert Costello, appeared to be a final opportunity for allies of the former president to steer the grand jury away from an indictment. 

He was invited by prosecutors to appear after saying that he had information to undercut the credibility of a former lawyer and fixer for Mr. Trump, Michael Cohen, who later turned against him and then became a key witness in the Manhattan district attorney’s investigation.

Mr. Costello had provided Cohen legal services several years ago after Cohen himself became entangled in the federal investigation into the hush money payments.

In a news conference after his grand jury appearance, Mr. Costello told reporters that he had come forward because he did not believe Cohen, who pleaded guilty to federal crimes and served time in prison, could be trusted.

“If they want to go after Donald Trump and they have solid evidence, then so be it,” Mr. Costello said. “But Michael Cohen is far from solid evidence.”

Responding to Mr. Costello’s claims on MSNBC later Monday, Cohen said that Mr. Costello was never his lawyer and “he lacks any sense of veracity.”

There were no clear signs that Mr. Costello’s testimony had affected the course of the investigation. Cohen had been available for over two hours in case prosecutors wanted him to rebut Mr. Costello’s testimony but was told he was not needed, his attorney said Monday.

The testimony came two days after Mr. Trump said he expected to face criminal charges and urged supporters to protest his possible arrest. 

In a series of social media posts through the weekend, the Republican former president criticized the New York investigation, directing particularly hostile rhetoric toward the Manhattan district attorney, Alvin Bragg, a Democrat.

New York officials have been monitoring online chatter of threats of varying specificity, and even as portable metal barricades were dropped off to safeguard streets and sidewalks, there were no immediate signs that Mr. Trump’s calls for protests were being heeded.

Mr. Costello briefly acted as a legal adviser to Cohen after the FBI raided Cohen’s home and apartment in 2018. At the time, Cohen was being investigated for both tax evasion and for payments he helped orchestrate in 2016 to buy the silence of two women who claimed to have had sexual encounters with Trump.

For several months, it was unclear whether Cohen, a longtime lawyer and fixer for the Trump Organization who once boasted that he would “take a bullet” for his boss, would remain loyal to the president.

Cohen ultimately decided to plead guilty in connection with the payments to porn actor Stormy Daniels and model Karen McDougal, which he said were directed by Mr. Trump. 

Since then, he has been a vociferous Trump critic, testifying before Congress and then to the Manhattan grand jury.

Mr. Trump, who has denied having sex with either woman, has branded Cohen a liar. Mr. Costello broke with Cohen before he pleaded guilty, after it became clear he was no longer in Trump’s camp.

In the years since, Costello, a veteran New York attorney, has represented Trump allies including his former political strategist, Steve Bannon, and his personal lawyer, Mayor Giuliani.

Even as the New York investigation pushes toward conclusion, Trump faces criminal probes in Atlanta and Washington that, taken together, pose significant legal peril and carry the prospect of upending a Republican presidential race in which Trump remains a leading contender. 

Some of his likely opponents have tried to strike a balance between condemning a potential prosecution as politically motivated while avoiding condoning the conduct at issue.

Governor Ron DeSantis, an expected GOP presidential candidate, criticized the investigation but also threw one of his first jabs at the former president in a move likely to intensify their simmering political rivalry.

“I don’t know what goes into paying hush money to a porn star to secure silence over some kind of alleged affair,” Mr. DeSantis said at a news conference in Panama City. “I can’t speak to that.”

Yet, he added, “what I can speak to is that if you have a prosecutor who is ignoring crimes happening every single day in his jurisdiction and he chooses to go back many, many years ago to try to use something about porn star hush money payments, that’s an example of pursuing a political agenda and weaponizing the office. And I think that’s fundamentally wrong.”