Former National Enquirer publisher David Pecker has testified at Donald Trump's criminal trial that he suppressed a story about an alleged affair to help Mr Trump's 2016 presidential bid, even though it would have boosted sales of his tabloid.

Testifying for a third day, Mr Pecker, 72, agreed with a prosecutor who asked whether it would have been "National Enquirer gold" to publish the story of former Playboy model Karen McDougal's claim that she had an affair with Mr Trump in 2006 and 2007.

But Mr Pecker said he opted not to run the story after paying Ms McDougal for it, because it would have hurt the Republican Trump's chances of winning the election over Democrat Hillary Clinton.

"You killed the story because it helped the candidate, Donald Trump?" prosecutor Joshua Steinglass asked him.

Mr Pecker said yes.

The exchange bolstered previous testimony in which Mr Pecker said he worked with Mr Trump's campaign to suppress allegations of adultery at a time when the then-presidential candidate was facing multiple accusations of sexual misbehavior.

Mr Pecker is the first witness in the case, which accuses Mr Trump, 77, of falsifying business records to cover up a hush money payment to adult film actress Stormy Daniels.

Mr Pecker has testified that his tabloid paid to "catch and kill" two such stories and alerted Mr Trump that Ms Daniels was also looking to sell her story of a sexual encounter with Mr Trump.

The defense has argued the payment was made to spare his family embarrassment, not bolster his campaign.

Mr Trump denies an encounter took place and has pleaded not guilty to the charges.

Under cross-examination, Trump lawyer Emil Bove sought to undermine Mr Pecker's credibility.

Donald Trump's defense lawyer Emil Bove

Mr Bove asked Mr Pecker whether he had inaccurately testified that Mr Trump thanked him at the White House for handling those negative stories.

That conflicted with a report by FBI agents who previously interviewed Mr Pecker, which said Mr Trump had not expressed gratitude.

Mr Pecker, 72, said the FBI report could be wrong.

"I know what I testified to, and I know what I remember," Mr Pecker told the court's 12 jurors and six alternates.

Mr Bove asked Mr Pecker whether his statements aligned with facts contained in an agreement by the Enquirer's parent company to cooperate with legal authorities to avoid prosecution. Mr Pecker denied any substantial mismatch.

Mr Bove has also sought to illustrate that Mr Pecker's checkbook journalism was not confined to Mr Trump.

Under questioning by Mr Bove yesterday, Mr Pecker said the Enquirer paid hundreds of thousands of dollars to obtain stories from women who came forward during Arnold Schwarzenegger's 2003 run for California governor to say they had affairs with him.

Mr Pecker said the first time he gave Mr Trump a heads up about a negative story was in 1998 in relation to Marla Maples, his wife at the time.

Prosecutors say Mr Pecker's arrangement with Mr Trump corrupted the 2016 election. He agreed to cooperate to avoid criminal charges.

Mr Trump is the first former president to face criminal charges. The trial, which is expected to run through May, could be the only one of his four criminal prosecutions to be completed before his 5 November election rematch with Democratic President Joe Biden.

One of those cases, which charges Mr Trump with trying to overturn his 2020 loss to Mr Biden, has been delayed for months by the US Supreme Court as it considers Mr Trump's argument that presidents should be immune for actions they take while in office.

In oral arguments yesterday, justices on the conservative-majority court signaled support that Mr Trump should have some level of protection from criminal charges.

Justice Juan Merchan, who is hearing the hush money case, has yet to rule on a request by prosecutors to punish Trump for allegedly violating a gag order that bars him from publicly criticising witnesses, some court officials and their relatives.

Judge Merchan said he would hold a hearing next Thursday to examine what prosecutors say are further gag order violations.

Mr Trump could be fined $1,000 for each violation or jailed, though prosecutors say they are not seeking imprisonment at this point.