Donald Trump’s criminal hush money trial resumes on Thursday with a former tabloid publisher testifying about efforts to help Mr Trump’s 2016 presidential bid by burying negative stories, including an alleged affair with a former Playboy model.

Former National Enquirer publisher David Pecker, 72, is a key witness in the case against the former US president, who is accused of falsifying business records documenting a $130,000 (€121,000) payment to porn star Stormy Daniels to keep her quiet about an affair she said she had with Mr Trump in 2006.

Mr Pecker, who has not been charged with a crime, testified on Tuesday that the Enquirer paid two people for stories of Mr Trump’s alleged sexual misbehaviour but never published them – a practice known as “catch and kill”.

He was expected to testify on Thursday about a similar payment to former Playboy model Karen McDougal, who said she had a yearlong affair with Mr Trump in 2006 and 2007.

Ms McDougal is also expected to testify during the trial, along with Trump’s former lawyer and fixer Michael Cohen, who says he arranged the Ms Daniels payment and was reimbursed by Mr Trump.

Mr Trump has pleaded not guilty to 34 felony counts and denied having an affair with Ms Daniels, whose real name is Stephanie Clifford. He has also denied having an affair with Ms McDougal.

Hush money payments themselves are not illegal, and Mr Trump’s lawyers have argued the Daniels payout was personal and unrelated to his campaign.

Prosecutors say that the payment was a campaign expense that should have been disclosed and that Mr Trump’s arrangement with the Enquirer deceived voters by suppressing stories of alleged extramarital affairs at a time when he faced accusations of sexual misbehaviour.

The trial is the first of a former US president and carries political risks for Mr Trump as he prepares for a November election rematch with US president Joe Biden and fends off three other criminal indictments to which he has also pleaded not guilty.

On Wednesday, he was named as an unindicted co-conspirator in an Arizona criminal case that charges 18 people with attempting to overturn his defeat in that state in the 2020 election.

Also on Thursday, the US Supreme Court is set to hear Mr Trump’s arguments that he is immune from prosecution for actions taken as president, an appeal that has held up his prosecution on charges related to his attempts to reverse his 2020 election defeat.

Mr Trump is required to be present for the New York trial and Justice Juan Merchan denied his request to attend the Supreme Court arguments.

“We have a big case today, the judge isn’t allowing me to go,” Mr Trump said while visiting a construction site on Thursday morning.

Mr Trump has complained that the trial, which is expected to last through May, is preventing him from campaigning though he uses his courthouse appearances as mini-stump speeches.

Judge Merchan has imposed a limited gag order on Mr Trump that bars him from publicly attacking witnesses, jurors and other people close to the case, including court staff and their families.

Prosecutors have asked Judge Merchan to fine Mr Trump $1,000 apiece for 10 social media posts they said violated the order, including one where he called Mr Cohen and Ms Daniels “sleazebags.”

Mr Trump has said the gag order violates his right to free speech and says he is being treated unfairly by Judge Merchan.