Donald Trump engaged in “a conspiracy and a cover-up”, a prosecutor has told jurors during closing arguments in the former US president’s hush money trial, while a defence lawyer branded the star witness as the “greatest liar of all time” and pressed the panel for an across-the-board acquittal.

The lawyers’ duelling accounts, wildly divergent in their assessments of witness credibility and the strength of evidence, offered both sides one final chance to score points with the jury before it starts deliberating the first felony case against a former American president.

“This case, at its core, is about a conspiracy and a cover-up,” prosecutor Joshua Steinglass told jurors.

The trial featured allegations that Trump and his allies conspired to stifle potentially embarrassing stories during the 2016 presidential campaign through hush money payments, including to an adult film actress who alleged that she and Trump had sex a decade earlier.

Trump has denied having sex with the actress, Stormy Daniels.

His lawyer Todd Blanche told jurors that neither Ms Daniels nor the Trump lawyer who paid her can be trusted in their evidence.

“President Trump is innocent. He did not commit any crimes, and the district attorney has not met their burden of proof, period,” Mr Blanche said.

Following more than four weeks of evidence, the day-long summations teed up a momentous and historically unprecedented task for the jury as it decides whether to convict the presumptive Republican presidential nominee ahead of the November election.

The political implications of the proceedings were unmistakable as President Joe Biden’s campaign staged an event outside the courthouse with actor Robert De Niro while Mr Blanche reminded jurors that the case was not a referendum on their views about Trump.

Mr Steinglass sought to defray potential juror concerns about witness credibility.

He acknowledged that Ms Daniels’ account about the alleged 2006 encounter in Lake Tahoe hotel suite was at times “cringeworthy” but said the details she offered – including about the decor and what she said she saw when she snooped in Trump’s toiletry kit – were full of touchstones “that kind of ring true”.

The story matters, he said, because it “reinforces (Trump’s) incentive to buy her silence”.

“Her story is messy. It makes people uncomfortable to hear. It probably makes some of you uncomfortable to hear. But that’s kind of the point,” Mr Steinglass said.

He told jurors: “In the simplest terms, Stormy Daniels is the motive.”

Mr Steinglass also tried to reassure jurors that the prosecution’s case did not rest solely on Michael Cohen, Trump’s former lawyer and personal fixer who paid Ms Daniels 130,000 dollars (£101,000) to keep quiet.

Mr Cohen later pleaded guilty to federal charges for his role in the hush money payments, as well as to lying to Congress.

He went to prison and was disbarred, but his direct involvement in the transactions made him a key witness at trial.

“It’s not about whether you like Michael Cohen. It’s not about whether you want to go into business with Michael Cohen. It’s whether he has useful, reliable information to give you about what went down in this case, and the truth is that he was in the best position to know,” Mr Steinglass said.

Trump faces 34 felony counts of falsifying business records, charges punishable by up to four years in prison.

He has pleaded not guilty and denied wrongdoing.

It is unclear whether prosecutors would seek imprisonment in the event of a conviction, or if the judge would impose that punishment.

Though the case featured seamy details about sex and tabloid industry practices, the actual charges turn on something more mundane: reimbursements Trump signed for Mr Cohen for the hush money payments.

The reimbursements were recorded as being for legal expenses, which prosecutors say was a fraudulent label designed to conceal the purpose of the hush money transaction and to illicitly interfere in the 2016 election.

Defence lawyers say Mr Cohen actually did substantive legal work for Trump and his family.

In his own hours-long address to the jury, with sweeping denials echoing Trump’s “deny everything” approach, Mr Blanche attacked the entire foundation of the case.

He said Mr Cohen, not Trump, created the invoices that were submitted to the Trump Organisation for reimbursement and that there was no proof that Trump knew what staff were doing with the payments.

He disputed the contention that Trump and Ms Daniels had sex, and he rejected the idea that the alleged hush money scheme amounted to election interference.

“Every campaign in this country is a conspiracy to promote a candidate, a group of people who are working together to help somebody win,” Mr Blanche said.

But as expected, he reserved his most animated attack for Mr Cohen, with whom he tangled during a lengthy cross-examination.

Mimicking the term “GOAT”, used primarily in sports as an acronym for “greatest of all time”, Mr Blanche labelled Mr Cohen the “GLOAT” – “greatest liar of all time”.

The lawyer also called Mr Cohen “the human embodiment of reasonable doubt”.

That language was intentional because, to convict Trump, jurors must believe that prosecutors proved their case beyond a reasonable doubt.

“He lied to you repeatedly. He lied many, many times before you even met him. His financial and personal wellbeing depend on this case. He is biased and motivated to tell you a story that is not true,” Mr Blanche said.

The lawyer’s voice became even more impassioned as he revisited one of the more memorable moments of the trial: when Mr Blanche sought to unravel Mr Cohen’s claim that he had spoken to Trump by phone about the Daniels arrangement on October 24 2016.

Mr Cohen said he had contacted Trump’s bodyguard as a way of getting hold of Trump, but Mr Blanche asserted that at the time Mr Cohen was actually dealing with a spate of harassing phone calls and was preoccupied with that problem.

“It was a lie,” Mr Blanche said.

“That was a lie, and he got caught red-handed.”

In his evidence, Mr Cohen acknowledged a litany of past lies, many of which he said were intended to protect Trump.

But he said he had subsequently told the truth, at great cost, saying: “My entire life has been turned upside-down as a direct result.”

Mr Steinglass used a bit of stagecraft to challenge the defence’s assertion that Mr Cohen was lying about the subject of that phone conversation, demonstrating a hypothetical version of the call to show jurors how Mr Cohen and the bodyguard, Keith Schiller, could have covered multiple subjects in less than a minute.

Mr Cohen’s actual call to Mr Schiller’s phone number lasted 96 seconds, according to phone records.

Mr Steinglass showed, with his hypothetical, that Mr Cohen could have spoken to Mr Schiller about the prank calls, asked him to pass the phone to Trump and then discussed the Daniels deal with Mr Trump, all in 49 seconds.

The New York prosecution is one of four criminal cases pending against Trump as he seeks to reclaim the White House from Mr Biden.

It is unclear if any of the others will reach trial before November’s election.