NEW YORK (Reuters - Donald Trump's lawyers on Thursday said Manhattan prosecutors improperly relied on evidence of the former U.S. president's official acts in securing his conviction on criminal charges stemming from hush money paid to a porn star.

His lawyers said the guilty verdict should be set aside following the U.S. Supreme Court's ruling on presidential immunity.

Justice Juan Merchan this month delayed Trump's sentencing by two months after defense lawyers said the justices' July 1 ruling that presidents cannot face criminal charges over official acts meant prosecutors should not have shown evidence from Trump's time in the White House at trial.

They said that meant the Manhattan jury's May 30 guilty verdict in the first-ever criminal trial of a U.S. president could not stand.

Prosecutors with Manhattan District Attorney Alvin Bragg's office have until July 24 to respond. They have previously called Trump's arguments meritless but agreed to push back the sentencing.

Legal experts said Trump faces steep odds of getting the hush money conviction overturned, since much of the case involves conduct before his presidency and the evidence from his time in the White House has more to do with private conduct.  

The Supreme Court's ruling stemmed from a separate case Trump faces on federal charges involving his efforts to undo his 2020 election loss to Joe Biden. It all but ensured Trump would not face trial in that case before the Nov. 5 election. 

Trump's lawyers are also seeking a pause in a third criminal case on charges of mishandling classified documents due to the ruling. Trump has pleaded not guilty to all charges.     

In the hush money case, Trump was found guilty of falsifying business records to cover up his former lawyer's $130,000 payment to adult film star Stormy Daniels to remain quiet about a sexual encounter she says she had with Trump. Prosecutors say the payment was designed to boost his presidential campaign in 2016, when he defeated Democrat Hillary Clinton.

Trump denies having had sex with Daniels and has vowed to appeal after his sentencing. 

The Supreme Court's decision said evidence of a president's official acts cannot be used in a prosecution on private matters.

Trump's lawyers say that means evidence such as a conversation he had with former White House aide Hope Hicks in 2018 about the Daniels payment and tweets he sent in 2018 about Cohen and Daniels was improper and tainted the verdict. 

Merchan has said he will decide on Trump's arguments by Sept. 6. If the conviction is upheld, Trump will be sentenced on Sept. 18 - less than seven weeks before the election. 

(Reporting by Luc Cohen in New York; Editing by Noeleen Walder and Jamie Freed)

By Luc Cohen