Seven jurors down, five more to go. The complicated process of picking a jury in the first criminal trial of an American president will continue for a third day on Thursday as lawyers on both sides choose the panel that will decide Donald J. Trump’s fate.

The case against Mr. Trump stems from a hush-money payment to a porn star, Stormy Daniels, who during the 2016 presidential campaign threatened to go public with her story of a sexual encounter with Mr. Trump. Prosecutors say Mr. Trump concealed her story, and others, to influence the election.

Mr. Trump has denied having sex with Ms. Daniels or breaking any laws. But prosecutors say he falsified business records to cover up the sex scandal, and charged him last year with 34 felony counts. If convicted, he faces up to four years behind bars.

Many expected jury selection to be a weekslong slog, but seven jurors were seated on Tuesday afternoon. Those initial members of the panel, four men and three women, reflect the diversity of the city they were drawn from: a man originally from Ireland who will serve as foreman, an oncology nurse, a grandfather originally from Puerto Rico, a middle-school teacher from Harlem, two lawyers and a software engineer for Disney. The judge in the case, Juan M. Merchan, has ordered the identities of the jurors be withheld from the public.

Once the 12 jurors are picked, the lawyers will shift to selecting several alternates who will sit through the entire case in the event that one of the main jurors gets sick or is forced to leave the panel.