The court on Thursday denied Trump's last-minute bid prevent his sentencing, scheduled for Friday morning in New York state court in Manhattan.
Trump had sought relief from the justices as he pursued a state court appeal to resolve questions of presidential immunity following a Supreme Court ruling last July that granted former presidents broad immunity from criminal prosecution for their official acts.
Trump was found guilty of 34 counts of falsifying records to cover up a payment to Stormy Daniels. (AP PHOTO)
The justices acted after New York's top court on Thursday rejected Trump's request to halt his sentencing.
Manhattan prosecutors made a filing at the Supreme Court on Thursday morning, opposing Trump's bid for a stay.
"Defendant now asks this court to take the extraordinary step of intervening in a pending state criminal trial to prevent the scheduled sentencing from taking place - before final judgment has been entered by the trial court, and before any direct appellate review of defendant's conviction. There is no basis for such intervention," Manhattan District Attorney Alvin Bragg's office wrote in a filing.
The trial judge in Trump's case, Justice Juan Merchan, said last week he was not inclined to sentence the Republican president-elect to prison and would likely grant him unconditional discharge. This would place a guilty judgment on Trump's record, but would not impose custody, a fine or probation.
Trump in a Supreme Court filing made public on Wednesday asked for proceedings in the case to stop as he seeks an appeal to resolve questions of presidential immunity following the Supreme Court's ruling last July that granted former presidents broad immunity from criminal prosecution for their official acts.
"This appeal will ultimately result in the dismissal of the District Attorney's politically motivated prosecution that was flawed from the very beginning," Trump's lawyer John Sauer wrote in the filing.
Sauer is Trump's pick to serve as US solicitor general, the government's chief lawyer at the Supreme Court.
Trump was found guilty last May of 34 counts of falsifying business records to cover up a $US130,000 ($A210,000) payment to porn star Stormy Daniels in exchange for her silence before the 2016 US election about a sexual encounter she has said she had with Trump a decade earlier, which he has denied. Prosecutors have said the payment was designed to help Trump's chances in the 2016 election, when he defeated Democrat Hillary Clinton.
Trump is the first former US president to be criminally prosecuted and the first former president convicted of a crime.
He has denied any wrongdoing.
Trump's lawyers contend that prosecutors improperly admitted evidence of Trump's official acts during the trial. They also argue that, as president-elect, Trump is immune from prosecution during the period between his November election victory and his inauguration.
In their filing on Thursday to the Supreme Court, the New York prosecutors said "all of the evidence defendant challenged in his post-trial motion either concerned unofficial conduct that is not subject to any immunity, or is a matter of public record that is not subject to preclusion, as the trial court correctly held".
As to Trump's argument that he is immune as president-elect, the prosecutors said this "extraordinary immunity claim is unsupported by any decision from any court".
"It is axiomatic that there is only one president at a time," they said..
