Jury selection in former President Donald Trump's historic criminal trial in New York will continue for a second day on Tuesday, when the process of seating potential jurors resumes as the defendant looks on.

The first batch of jurors were sworn in on Monday after pretrial arguments over evidence and rules for the proceedings. Roughly two thirds of the group of 96 New Yorkers were quickly dismissed, with most of them saying they wouldn't be able to be fair and impartial in the trial. Others were excused for various other reasons, including their answers to a list of questions posed to each juror.

Prosecutors and defense attorneys may also briefly argue Tuesday, without jurors present, over what topics prosecutors can question Trump about if he chooses to testify in his own defense later in the trial.  

The slow process of identifying suitable jurors is likely to last at least a week. More jurors will face questioning when the second day of proceedings kicks off at 9:30 a.m.

Trump, the presumptive Republican nominee for president, is charged with 34 state felony counts of falsification of business records related to a "hush money" payment his attorney made to adult film star Stormy Daniels before the 2016 election. He has pleaded not guilty to all charges, claiming the prosecution is part of a plot by Democrats aimed at preventing him from retaking the White House. The case is the first of four criminal prosecutions against Trump to make it to trial.

The first day of the trial also featured a series of rulings by Judge Juan Merchan, who is overseeing the case. He sided with prosecutors from Manhattan District Attorney Alvin Bragg's office on several matters, and ruled for Trump's attorneys on other questions. 

At several points during Monday morning's pretrial arguments, Trump appeared to fall asleep at the defense table, his chin dropping to his chest briefly. In one instance, he was stirred awake by his attorney.

The trial is expected to last between six and eight weeks, convening every weekday except Wednesdays, with some shortened days for the Passover holiday. The schedule severely limits Trump's ability to hit the campaign trail, which he has cited to support his claims of political bias. 

Merchan made clear that Trump is expected to attend each day of the trial, and said he would face arrest if he fails to appear. He denied a request by defense attorneys to allow Trump to attend Supreme Court arguments over his claim of presidential immunity in one of his federal cases next week.

"Your client is a criminal defendant in New York County Supreme court. He is required to be here. He is not required to be in the Supreme Court. I will see him here next week," Merchan told one of Trump's lawyers.