Former President Donald J. Trump sought to move his Manhattan criminal case into federal court on Thursday, filing the unusual request three months after he was convicted in state court.

The long-shot bid marks Mr. Trump’s latest effort to stave off his sentencing in state court in his hush-money trial, in which he was convicted of falsifying records to cover up a sex scandal.

He is scheduled to receive his punishment on Sept. 18, just seven weeks before Election Day, when he will square off against Vice President Kamala Harris for the presidency.

“The ongoing proceedings will continue to cause direct and irreparable harm to President Trump — the leading candidate in the 2024 presidential election — and voters located far beyond Manhattan,” Mr. Trump’s lawyers, Todd Blanche and Emil Bove, wrote in the filing.

Their filing came even as the Trump legal team is awaiting the result of a separate effort to postpone the sentencing; it opened a second front that could complicate the first.

On Aug. 15, Mr. Trump asked the state court judge who presided over the trial, Juan M. Merchan, to delay the sentencing until after Election Day. Mr. Trump’s lawyers argued that they needed more time to challenge his conviction on the basis of a recent Supreme Court ruling granting presidents broad immunity for official acts.

The Manhattan district attorney’s office, which won the conviction of Mr. Trump on May 30, has argued that the Supreme Court’s ruling has “no bearing” on their case, which centers on Mr. Trump’s cover- up of a sex scandal involving a porn star. But the Manhattan prosecutors deferred to the judge on whether to delay the sentencing, leaving the door open for Justice Merchan to punt until after the election.

Justice Merchan was expected to rule on the delay request next week, and it is unclear whether Mr. Trump’s federal petition would disrupt that. In the federal filing, the former president’s lawyers asked a judge to find that Justice Merchan was barred by law from sentencing Mr. Trump while their attempt to move the case was underway.

It seemed possible that effort might backfire. If the federal judge does not grant the lawyers’ request, they will have further alienated Justice Merchan as he prepares to sentence their client. Mr. Trump faces up to four years in prison, though he could receive a shorter sentence, or merely probation.

There are signs the federal judge might be skeptical. Mr. Trump already tried — and failed — to move the case to federal court. Last year, soon after the former president was indicted, he asked the same federal judge to remove the case from Justice Merchan, arguing that it concerned official acts as president.

The judge, Alvin K. Hellerstein, rejected that argument.

“The evidence overwhelmingly suggests that the matter was a purely personal item of the president — a cover-up of an embarrassing event,” Judge Hellerstein wrote in an opinion last year. “Hush money paid to an adult film star is not related to a president’s official acts. It does not reflect in any way the color of the president’s official duties.”

It is unclear how soon Judge Hellerstein might take up Thursday’s request, or whether he will hold a hearing to entertain it. In their filing, Mr. Trump’s lawyers cast aspersions on the New York State court system, saying its procedures had “proven inadequate” to protect federal interests and, if allowed to continue, would “result in further irreparable harm to President Trump.”

The unorthodox filing suggested that Mr. Trump’s lawyers are likely to make any and every attempt they can to delay the sentencing, even if Judge Hellerstein balks.

A spokeswoman for the district attorney’s office declined to comment.

The filing on Thursday captured two of Mr. Trump’s favorite legal strategies: delay, and attacks on Justice Merchan.

The former president has on three occasions sought to oust Justice Merchan from the case, claiming he is biased, and lobbing personal attacks at the judge’s daughter, who is a Democratic political consultant. The judge has rejected each request and assailed the claims as “rife with inaccuracies and unsubstantiated claims.”