Writer E Jean Carroll is accusing the former US president of defaming her in 2019 by denying he had attacked her in a department store dressing room.
Trump, who has said he wants to testify at the civil trial, sat two tables behind Carroll, who is accusing him of defaming her in 2019 by denying he had attacked her in a Bergdorf Goodman department store dressing room in Manhattan.
Carroll, 80, is seeking at least $10m in damages.
US District Judge Lewis Kaplan, who is overseeing the case, told prospective jurors on Tuesday that they would only have to consider how much Trump should pay Carroll in damages, not whether the alleged assault took place or whether Trump lied about it.
He added that the trial is expected to last three to five days.
Trump has cast himself as the victim of political persecution and said Kaplan should dismiss the case.
“Judge Kaplan should put this whole corrupt, Crooked Joe Biden-directed Election Interference attack on me immediately to rest,” he said on social media.
“He should do it for america.”
Trump has so far pleaded not guilty in four criminal cases that could potentially land him in prison before the November presidential election, including two that accuse him of trying to overturn the results of the 2020 election.
He is also the defendant in at least two other civil cases. But Trump has already lost one defamation case against Carroll.
In May last year, a jury ordered Trump to pay the former Elle columnist $5m for having sexually abused her during the encounter and defaming her.
Trump has said that he did not know Carroll and that she made up the encounter to sell her memoir. He is also appealing the $5m award.
Kaplan, who also presided over that case, said he has barred Trump from arguing that he did not defame or sexually assault Carroll or that she made up her account.
In recent weeks, Trump has ramped up his attacks on Carroll, including saying she did not know the decade of their encounter.
He also called Kaplan “terrible, biased, irrationally angry”.
Trump may face an uphill fight to escape significant additional damages because of Kaplan’s pre-trial rulings.
These include banning Trump from suggesting he did not rape Carroll, as New York’s penal law defines the term, because the first jury did not find that Trump committed rape.
Kaplan has ruled that because Trump used his fingers in the assault, Carroll’s rape claim was “substantially true.”
Trump also cannot discuss DNA evidence or Carroll’s sexual activities, or suggest that Democrats are bankrolling her case. Carroll is a Democrat.
And as happened at the first trial, jurors will be able to see the 2005 video from Access Hollywood video where Trump graphically described the ability of famous people like himself to have sexual relations with beautiful women.
Trump did not retract his comments when asked about them in a 2022 deposition. Kaplan has said the video could offer “useful insight into Mr. Trump’s state of mind” toward Carroll.
Trump lawyer Alina Habba on Sunday assured Kaplan that he was “well aware” of the court’s rulings “and the strict confines placed on his testimony”.