NEW YORK — A New York judge on Thursday rejected a second request by former President Donald Trump to declare a mistrial over the testimony of porn actress Stormy Daniels.

State Supreme Court Judge Juan Merchan said the defense opened the door to Ms. Daniels’ salacious testimony by denying her claim of a sexual encounter during its opening statement.

“Right off the bat, that puts your client’s word against Ms. Daniels’ word,” the judge said.

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The judge also refused to exclude the porn star from a gag order against Mr. Trump in the case, saying he remains worried about reprisals against witnesses and the integrity of the trial as a whole.

Defense Todd Blanche said Ms. Daniels went too far in describing her alleged sexual encounter with Mr. Trump in 2006 and that her testimony was inconsistent with the story she told Michael Cohen, who was Mr. Trump’s lawyer and will be a key witness for the prosecution. 

Also, Ms. Daniels described her relative height versus Mr. Trump from the witness stand — information that could create the impression of a “power imbalance” during the alleged sexual encounter.

“None of that information is information that goes to the motive of anybody in this case,” Mr. Blanche said.

The prosecution said the defense was not ambushed by Ms. Daniels, pointing to details in investigative notes and Ms. Daniels’ past interviews.

“All of which the defense has had access to,” prosecutor Joshua Steinglass said.

Mr. Steinglass said the defense is trying to argue that Ms. Daniels’ story is false while preventing her from offering corroborating testimony.

“They’re trying to have their cake and eat it too,” he said.

In denying the motion, the judge said he struck problematic testimony from the record.

And he said Mr. Trump’s attorneys did not object when they should have, including to a reference about whether Mr. Trump wore a condom.

Mr. Blanche also said Mr. Trump should get a carve-out from his gag order for Ms. Daniels since she is done testifying and has a tendency to ridicule Mr. Trump publicly while he runs for president.

“He needs an opportunity to respond to the American people,” Mr. Blanche said, adding Mr. Trump will be asked questions about the testimony.

Prosecutors objected, saying the gag order is needed to keep Mr. Trump from intimidating other potential witnesses and chilling their involvement. 

Mr. Trump is banned from opining on witnesses, jurors, or certain court staff and has been fined 10 times for violations.

“There are people making the defendant’s case for him out in the world,” prosecutor Christopher Conroy said.

Mr. Conroy said witnesses in the case have real fears about reprisals, citing a witness’s reaction to seeing her home address on a record in the case.

“You could see the fear in her eyes when that happened,” he said.

On Mr. Trump, the prosecutor said, “Let’s not pretend he wants to engage in high-minded discourse.”

Judge Merchan said he could not take Mr. Blanche’s word that Mr. Trump would not attack a broad swath of witnesses.

“My concern is not just with protecting Ms. Daniels, my concern is with protecting these proceedings as a whole,” Judge Merchan said. “Witnesses who have not yet testified will see what happens.”