More potential jurors have been dismissed from Donald Trump’s hush money case as lawyers worked for a second day to find a panel of New Yorkers to decide whether the Republican will become the first former US president convicted of a crime.

The first day of the historic trial in Manhattan ended on Monday with no-one yet chosen to be on the panel of 12 jurors and six alternates.

In short order on Tuesday morning, several others were excused after saying they could not be impartial or because they had other commitments.

Dozens of potential jurors have yet to be questioned.

It is the first of Trump’s four criminal cases to go to trial and may be the only one that could reach a verdict before voters decide in November whether the presumptive Republican presidential nominee should return to the White House.

The trial puts Trump’s legal problems at the centre of the closely contested race against President Joe Biden.

Trump paints himself as the victim of a politically motivated justice system working to deprive him of another term.

It also presents a major test for the criminal justice system because the allegations are being viewed through a partisan lens, and Trump’s attacks on prosecutors and the judge threaten to undermine the public’s faith in the courts.

Trump has pleaded not guilty to 34 felony counts of falsifying business records as part of an alleged effort to keep salacious – and, he says, bogus – stories about his sex life from emerging during his 2016 campaign.

Trump arrived at court just before 9am, giving a quick wave to reporters as he headed inside.

Before entering the courtroom, Trump stopped briefly to address a TV camera in the hallway, repeating his claim that the judge is biased against him and the case is politically motivated.

“This is a trial that should have never been brought,” Trump said.

After he went inside, reporters saw him wink at one of the court officers and mouth “How are you?” while he walked down the aisle.

Trump then took his seat at the defence table with his lawyers.

One woman in the jury pool was let go after previously notifying the judge during Monday’s questioning that she had a trip planned around Memorial Day.

A man was excused after saying he could not be impartial.

Another man, who works at an accounting firm, was dismissed after saying he feared his ability to be impartial could be compromised by “unconscious bias” from growing up in Texas and working in the finance world with people who “intellectually tend to slant Republican”.

After another juror said she would be unable to serve impartially, Trump twisted in his chair, looking in the direction of the box.

Through the first few minutes of the day, he appeared generally attentive, jotting down notes and raising sheets of paper to his face as jurors rattled off answers to a lengthy questionnaire.

The charges centre on 130,000 dollars (£104,400) in payments that Trump’s company made to his then-lawyer, Michael Cohen.

He paid that sum on Trump’s behalf to keep adult film actor Stormy Daniels from going public with her claims of a sexual encounter with Trump a decade earlier.

Trump has denied the sexual encounter ever happened.

Prosecutors say the payments to Mr Cohen were falsely logged as legal fees.

Prosecutors have described it as part of a scheme to bury damaging stories Trump feared could help his opponent in the 2016 race, particularly as Trump’s reputation was suffering at the time from comments he had made about women.

Trump has acknowledged reimbursing Mr Cohen for the payment and that it was designed to stop Ms Daniels from going public about the alleged encounter.

But Trump has previously said it had nothing to do with the campaign.

“I was paying a lawyer and marked it down as a legal expense,” he said.

“That’s exactly what it was. And you get indicted over that? I should be right now in Pennsylvania, in Florida, in many other states – North Carolina, Georgia – campaigning,” Trump told reporters on Tuesday.

Jury selection could take several more days – or even weeks – in the heavily Democratic city where Trump grew up and catapulted to celebrity status decades before winning the White House.

Only about a third of the 96 people in the first panel of potential jurors brought into the courtroom on Monday remained after the judge excused some members.

More than half of the group was excused after telling the judge they could not be fair and impartial, and several others were dismissed for other reasons that were not disclosed.

Another group of more than 100 potential jurors sent to the courthouse on Monday has not yet been brought into the courtroom for questioning.

In court papers filed on Tuesday, prosecutors urged the judge to fine Trump 3,000 dollars (£2,410) over social media posts they say violated a gag order limiting what he can say publicly about witnesses.

In the posts, Trump called Mr Cohen and Ms Daniels “two sleaze bags who have, with their lies and misrepresentations, cost our Country dearly!”

Prosecutors wrote that the judge should admonish Trump to comply with the gag order and warn him that further violations could be punished not only with additional fines but also jail time.

If convicted of falsifying business records, Trump faces up to four years in prison, though there is no guarantee he will get time behind bars.

Trump’s cases involving allegations of election interference and hoarding classified documents could lead to lengthy prison sentences, but those cases are tied up with appeals or other issues that make it increasingly unlikely they will be decided before the election.

And if Trump wins in November, he could presumably order a new attorney general to dismiss his federal cases.