"No sir I can't, because I am not certain that is accurate," Cohen responded. 

He said he believed that he spoke with Trump's then-bodyguard Keith Schiller about the harassment and also spoke briefly with Trump about the payment.

"We are not asking for your belief," Blanche said, raising his voice.

The exchange followed several hours of questioning by Blanche designed to cast Trump's former fixer as a spiteful turncoat eager to see his former boss behind bars.

Blanche played jurors audio clips of Cohen saying that the case "fills me with delight" and that he felt "giddy with hope and laughter" imagining Trump and his family in prison.

He told them that Cohen had previously lied to Congress and to the US Justice Department and had lied in court as well. 

He pointed out that Cohen had privately sought a pardon from Trump while publicly saying he would not accept one.

Cohen agreed that he had blamed others, including Trump, following his own criminal convictions on tax and campaign-finance charges.

"Does the outcome of this trial affect you personally?" Blanche asked.

"Yes," Cohen said, maintaining his composure while answering questions, in contrast with his aggressive and often profane public comments.

Trump has pleaded not guilty in the first criminal trial of a former US president and denies having a sexual encounter.

The New York case, one of four criminal prosecutions he faces, is likely to be the only one with a jury verdict before his November 5 election rematch with Democratic President Joe Biden.

Cohen's testimony is central to the case.

He testified earlier this week that Trump ordered him to pay Daniels to protect Trump's presidential campaign, and discussed a plan to reimburse Cohen through a series of bogus invoices for legal fees. 

Their chats included one in the White House Oval Office when Trump was president in 2017, Cohen said.

Trump, 77, faces 34 counts of falsifying business records in New York to cover up a payment to the porn star in the run-up to the 2016 presidential election.

Prosecutors say the altered records covered up election-law and tax-law violations - since the money was essentially an unreported contribution to Trump's campaign - that elevate the crimes from misdemeanours to felonies punishable by up to four years in prison.

Trump characterises the case and three other prosecutions as an attempt to interfere with his campaign to take back the White House.

Members of the libertarian-leaning US House of Representatives Freedom Caucus attended the trial on Thursday and echoed his complaints.

"We're seeing today what lengths the Democratic Party will go to to try to rig or steal another election," the group's chairman, Republican Representative Bob Good, said outside the courthouse.

Cohen carries significant baggage as a witness. 

He pleaded guilty in 2018 to campaign-finance and tax violations related to the Daniels payment and lying to Congress during an investigation into Trump's Russian government ties. 

He told jurors on Tuesday he lied repeatedly to journalists and others about the Daniels scandal.

Cohen's testimony has been corroborated by other evidence, including handwritten notes outlining Cohen's reimbursements and a surreptitious recording made by Cohen of Trump seeming to discuss a hush money payment made by the National Enquirer tabloid to another woman.

Blanche has said he expects his cross-examination of Cohen to last most of Thursday, meaning the defence would have the opportunity to call its own witnesses when the trial resumes next week.

 Trump has yet to decide whether to testify, he said.

Trump has argued that his monthly payments to Cohen throughout 2017 were for his work as his personal lawyer to the president, meaning there was nothing improper about the word "retainer" being written on the cheques Trump signed.

Prosecutors say the reimbursement payments were falsely labelled as legal expenses in the Trump Organization's records to conceal the Daniels pay-off, which they say violated US election campaign finance law.