Witness testimony has begun for a fourth day in former United States President Donald Trump’s New York trial related to hush-money payments made to an adult film star.

Trump’s lawyers on Friday are questioning former tabloid publisher David Pecker, who has spent three days detailing how he entered into a deal with Trump to “catch and kill” negative stories to try to help the ex-president’s 2016 White House campaign.

US prosecutors have spent days trying to establish a wider pattern of efforts by Trump to seek to illegally influence that year’s election.

Trump has been charged with 34 felony counts of falsifying business documents related to payments made to adult film star Stormy Daniels.

The charges concern the alleged mislabelling of repayments that Trump made to his lawyer Michael Cohen, who had paid $130,000 to Daniels in return for her silence over an alleged sexual encounter with Trump. The former president has denied the affair took place.

For the felony charges to hold, prosecutors must persuade the jury that the misrepresentations were done with the intent to commit or cover up another crime. They have primarily focused on what they called “election fraud, pure and simple”.

Trump’s defence team has argued that he did nothing illegal to justify the felony charges.

In the first portion of cross-examination on Thursday, Trump’s lawyer sought to portray agreements to “catch and kill” negative stories related to prominent individuals as “standard operating procedure”.

Pecker said similar deals had been made with Rahm Emanuel, the chief of staff to former President Barack Obama, and Arnold Schwarzenegger, the former governor of California.

Prior to that, prosecutors had focused on how Pecker had agreed to be the Trump campaign’s “eyes and ears”.

During questioning, Pecker said Trump never mentioned concerns about his family when discussing efforts to stifle claims of an alleged affair by model Karen McDougal as well as Daniels.

That appeared aimed at undercutting a central tenant of Trump’s defence: that he was seeking to stop personally damaging allegations from going public but not seeking to influence the election.

Prosecutors were also awaiting a decision from Judge Juan Merchan on whether Trump had violated a partial gag order in the case, which prevents him from publicly discussing individuals involved in the legal proceedings.

On Tuesday, they presented 10 such alleged violations, and prosecutors said on Thursday that Trump had committed four more since then.

They have called for Trump to be reprimanded for the violations.