Lawyers for the defence and the prosecution still must select alternate jurors for the trial, the first ever in which a former US president is the defendant.

Opening statements could take place on Monday, said Justice Juan Merchan, the judge overseeing the trial.

Earlier on Thursday, Merchan dismissed a juror who said she felt intimidated that some personal information was made public.

The judge also excused another juror after prosecutors said he may not have disclosed prior brushes with the law.

Trump's outsized public presence created unique problems during the jury selection process, which started on Monday.

Roughly half the first 196 jurors screened in heavily Democratic Manhattan were dismissed after saying they could not assess the evidence impartially.

The Republican politician's criticism of witnesses, prosecutors, the judge and their relatives in this case and others has also sparked concerns about harassment, prompting Merchan to impose a partial gag order.

Merchan dismissed the juror who said she felt intimidated after family, friends and colleagues had deduced she had been selected for the trial.

"I don't believe at this point that I can be fair and unbiased, and let the outside influences not affect my decision-making in the courtroom," the juror said.

Trump, the Republican presidential candidate in the November 5 election, also faces criminal cases in Washington, Georgia and Florida, but the New York case is the only one certain to go to trial this year.

Officials involved in those cases have reported receiving death threats and harassment after being criticised by Trump.

Trump has pleaded not guilty in all four cases and has said, without evidence, they are part of a broad-ranging effort by allies of Democratic President Joe Biden to hobble his candidacy.

A conviction would not bar him from taking office.

In New York, Trump is accused of covering up a $US130,000 ($A200,000) payment his former lawyer Michael Cohen made to porn star Stormy Daniels for her silence before the 2016 election about a sexual encounter she says they had a decade earlier.

Trump has pleaded not guilty to 34 counts of falsifying business records brought by Manhattan District Attorney Alvin Bragg and denies any such encounter with Daniels, whose real name is Stephanie Clifford.

Cohen pleaded guilty to campaign finance violations in 2018 and served prison time for making those payments, and Trump's lawyers are expected to attack his credibility as a witness.

Merchan has taken steps to shield jurors in the case from harassment, saying they will remain anonymous except to Trump, his lawyers and prosecutors.

On Thursday, he said he would prohibit news outlets from reporting on aspects of potential jurors' employment.

Prosecutors say Trump has violated Merchan's gag order seven times since they flagged three potential violations on Monday, and have asked the judge to impose fines or other penalties.

On Thursday, prosecutor Christopher Conroy pointed to posts saying undercover liberal activists had been lying to the judge to try to get on the jury.

One of Trump's lawyers, Emil Bove, said those posts "do not establish any willful violations" of the gag order.

Australian Associated Press