A federal judge on Wednesday ordered that the writer E. Jean Carroll should promptly receive a $5 million jury award, days after the Supreme Court rejected an appeal by President Trump and despite his last-minute attempt to get the justices to reconsider.

In a two-page order, Judge Lewis A. Kaplan of Manhattan federal court cited the Supreme Court’s June 29 order denying Mr. Trump’s request that the justices review the matter. That cleared the way for the funds, which Mr. Trump had deposited with the court, to be released to Ms. Carroll.

A Manhattan jury awarded the multimillion-dollar judgment to Ms. Carroll in May 2023 after finding him liable for sexually assaulting her in a Manhattan department store in the 1990s. The jury also found that Mr. Trump defamed Ms. Carroll by calling her allegations against him “a Hoax and a lie” on social media. He has continued to deny assaulting Ms. Carroll.

The Supreme Court did not announce its reasons for rejecting Mr. Trump’s appeal last week, which is typical when the court declines a petition to take on a case, and no public dissents were noted. Under the court’s rules, if the justices deny a petition, the parties have 25 days to request a rehearing.

Lawyers for Mr. Trump filed such a request earlier on Wednesday, again urging the justices to hear his appeal and saying they should take up the matter alongside a separate appeal in a second case involving Ms. Carroll.

It is rare but not unheard-of for the justices to grant such requests. But legal experts say in this case it might have been a last-ditch effort to stall Ms. Carroll from getting the jury’s award.

Stephen I. Vladeck, a professor at Georgetown University Law Center, said that “some of this appears to be a transparent play for time.”

After the court’s rejection last week, Ms. Carroll had immediately asked a federal judge to order the president to pay her, asserting that Mr. Trump had “consistently sought to obstruct and delay payment” of the jury’s award.

The court wrapped up its term last week and is now in summer recess. Although the justices continue to hear emergency applications, they are not scheduled to meet to consider other cases until September. That is when the justices will convene as they prepare to begin a new term, which officially starts on the first Monday in October. As a result, they may not consider Mr. Trump’s new request for months.

By then, the court may also need to decide whether to review a second case related to Ms. Carroll and Mr. Trump. Lawyers for Mr. Trump said in their petition on Wednesday that the president “will imminently file” to ask the justices to step in and overturn the verdict of a separate jury, which in 2024 had ordered him to pay Ms. Carroll $83.3 million after concluding Mr. Trump had defamed her in 2019.

In the petition, Mr. Trump’s lawyers asserted that the two cases are intertwined and said the justices should decide whether to hear them both at the same time.

Mr. Trump’s lawyers on Wednesday filed a notice indicating they would appeal Judge Kaplan’s order.