Justice Juan Merchan did not immediately rule on the request, which is routine in criminal trials and rarely granted. But he suggested that savvy jurors would be able to assess the credibility of Trump's ex-fixer's testimony for themselves.
"You said that his lies are irrefutable, but do you think he's going to fool 12 New Yorkers?" Merchan asked Trump lawyer Todd Blanche, who had sought the dismissal.
The exchange came at the end of a day in which questions about Cohen's character were front and centre. At the outset on Monday, Merchan said he expected the two sides to make their closing arguments next week followed by jury deliberations.
Donald Trump watched as his former 'fixer' Michael Cohen admitted stealing from him. (AP PHOTO)
The first former president to face a criminal trial, Trump has pleaded not guilty to 34 counts of falsifying business records to cover up a $US130,000 payment to silence porn star Stormy Daniels, who had threatened to go public before the 2016 presidential election with her account of an alleged sexual encounter - a liaison Trump denies.
Trump, 77, has blasted the trial as a politically motivated effort to hobble his Republican Party campaign to take back the White House from Democratic President Joe Biden at the US election.
Cohen, Trump's estranged former fixer and lawyer, testified that he spoke repeatedly with Trump about the payment to Daniels in the final stretch of the 2016 presidential campaign - a pillar of the prosecution's case.
But Trump's lawyers also got Cohen to admit that he stole money from his former boss because he was angry that his annual bonus fell short of his expectations after he handled the payment to Daniels.
He said he paid roughly $US20,000 in cash in a paper bag to a tech company out of the $US50,000 that it was owed and kept the rest. The Trump Organisation later reimbursed him $US100,000 in total to account for the taxes Cohen would owe.
"I just felt it was almost like self-help," Cohen said on the witness stand.
As a convicted felon and admitted liar, Cohen, 57, carries baggage as a witness. Formerly a zealous defender of Trump, he has become a fierce and frequently foul-mouthed critic.
Blanche said the case should be dismissed because Cohen was not credible.
"There is no way that the court should let this case go to the jury relying on Cohen's testimony," Blanche said outside the presence of the jury, adding that without Cohen's testimony "there is no case."
Prosecutor Christopher Conroy countered that Cohen's testimony was backed up by documents and other evidence.
"The trial evidence overwhelmingly supports each element of the offence," Conroy said. The judge could rule at any time on the motion to dismiss.
Earlier, with the prosecution having rested, Trump's lawyers began calling witnesses of their own.
One of those witnesses drew a reprimand from Merchan after he expressed dissatisfaction.
"If you don't like my ruling, you don't give me side eye and you don't roll your eyes," Justice Juan Merchan told Robert Costello, a lawyer.
Costello testified that Cohen told him after a 2018 FBI raid that he did not have any dirt on Trump to offer prosecutors.
"He said, 'I swear to God, Bob, I don't have anything on Donald Trump,'" Costello said, citing Cohen.
Costello also said Cohen told him numerous times that Trump knew nothing about the payment to Daniels.
Cohen has previously testified that he lied to Costello because he was worried he would relay to Trump any indications that he might cooperate with prosecutors.
It was as yet unclear whether Trump would testify when the trial resumes on Tuesday.
