NEW YORK — Prosecutors told jurors on Tuesday their star witness, Michael Cohen, remains a credible voice against former President Donald Trump despite his history of lying and apparent inconsistencies on the witness stand.

Assistant District Attorney General Joshua Steinglass put on a show to prove his point, holding up his hand like a mock telephone and recreating a pivotal phone call between Mr. Cohen and Mr. Trump’s bodyguard, Keith Schiller.

The defense says Mr. Cohen lied from the witness stand by claiming Mr. Trump signed off on a payment to porn star Stormy Daniels in the October 2016 call, when the call really seemed to focus on his complaints to Mr. Schiller about a young prank caller. Mr. Steinglass said it could be both, play-acting a call in which he addresses the pranker and Ms. Daniels.

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“49 seconds,” Mr. Steinglass said when he was done, indicating how quick it could be.

Mr. Trump’s lawyers have made Mr. Cohen’s credibility the crux of the defense.

Mr. Steinglass said prosecutors didn’t choose Mr. Cohen out of thin air or “pick him up at the witness store,” and he argued Mr. Trump hired Mr. Cohen years ago because of his penchant for cheating and lying.

Prosecutors say Mr. Trump paid Mr. Cohen $420,000 in 2017 to cover the Daniels payment, a bonus for Mr. Cohen and payments for tech services from the Red Finch company, plus a “grossing up” of the amount to account for taxes.

Mr. Blanche said the idea that Mr. Trump paid Mr. Cohen $420,000 when he owed him $130,000 “is absurd.” He also slammed Mr. Cohen for admitting he siphoned $30,000 of the $50,000 that he was paid to satisfy an invoice from Red Finch, saying the theft is a felony that further damages his credibility.

Mr. Steinglass said the told on itself by slamming Mr. Cohen’s theft even as it argued the checks were payments for general legal services.

“They can call him a thief or claim this wasn’t really a reimbursement,” Mr. Steinglass said, “but not both.”

Prosecutors allege Mr. Trump used Mr. Cohen to pay $130,000 to Ms. Daniels near the 2016 election because she was shopping a story about an alleged sexual encounter with Mr. Trump in 2006. They say Mr. Trump orchestrated an illegal plot to conceal repayment to Mr. Cohen to cover up another unidentified crime.

Mr. Trump is charged with 34 counts of falsifying business records with an intent to conceal that unnamed crime.

Trump defense lawyer Todd Blanche told jurors Tuesday they “should want and expect more” from prosecutors who claim the presumptive GOP nominee engaged in business fraud to boost his first run for the White House. He said the state’s evidence showed little more than standard business practices such as procuring a non-disclosure agreement.

Mr. Steinglass said there was a mountain of evidence that connected Mr. Trump to the scheme. The prosecution, during its closing, said Mr. Cohen was like a “tour guide” who could be trusted to say what invoices and checks in evidence mean, even if he had an axe to grind against his former boss.

“To date, he’s the only one who paid the price for this,” he said. “When it got bad, the defendant cut him loose, dropped him like a hot potato.”