Two jurors selected for Donald Trump's historic criminal trial were excused on Thursday as prosecutors and defence attorneys struggled to fill a panel to sit in judgment of the deeply polarizing former US president.

Judge Juan Merchan, who is presiding over the blockbuster case in New York, is hoping to find 12 jurors and six alternates by the end of the week and have opening arguments on Monday.

But the proceedings suffered a setback on Thursday as two already-chosen jurors were excused -- one because she had concerns her identity has been revealed and the other following doubts about the accuracy of some of his answers during questioning.

Trump, 77, who is seeking to recapture the White House in November, is accused of falsifying business records on the eve of his 2016 election victory to cover up a sexual encounter with a porn star.

He has pleaded not guilty.

Seven jurors had been selected as of Tuesday but that number fell to five on Thursday following the release of the two jurors who had already been sworn in.

To protect the anonymity of the New Yorkers randomly selected for jury service, Merchan asked reporters on Thursday to stop providing a physical description of potential jurors and not identify where they work.

A unanimous verdict will be required to convict Trump, and prosecutors and his attorneys are subjecting prospective jurors to intensive questioning as they seek to fashion a panel to their liking.

Potential jurors are being grilled, for example, about their media consumption, political donations, education and whether they have ever attended a pro- or anti-Trump rally.

About half of the first batch of 96 jurors ushered into the courtroom on Thursday were immediately excused after stating they would be unable to be fair and impartial in a case involving one of the most famous and controversial men in the country.

One potential juror said he was born and raised in Italy and "the Italian media have had a very strong association with Mr Trump and Silvio Berlusconi," the late Italian prime minister.

"It would be a little hard for me to retain my impartiality and fairness," he said.

He was excused. Trump motorcaded to the Manhattan courthouse from his luxury apartment building and -- breaking with his past practice -- did not address waiting reporters on his arrival.

He also did not speak as he left for lunch but flashed a thumbs-up.