The Trump administration on Monday asked the Supreme Court to clear the way for an executive order by President Trump that restricts voting by mail, setting up a legal showdown as the president pushes for more control over voting ahead of the midterm elections in November.

The administration filed the emergency application to the justices after a federal appeals court on Saturday blocked key parts of his executive order.

In the application, Solicitor General D. John Sauer called the lower court ruling “indefensible,” asserting that it imposed “serious irreparable harm on the federal government” and would bar federal agencies from implementing an executive order “promoting election integrity in the upcoming federal elections in November.”

The legal battle stems from an executive order signed up Mr. Trump in late March that had attempted to place limits on mail-in voting, including using federal oversight of the U.S. Postal Service to gain greater control over mail-in voting practices.

The executive order directed the Department of Homeland Security to create state-by-state citizen lists that would help determine voter eligibility. It then called on the Postal Service to use lists provided by states to determine if voters should be allowed to vote by mail.

More than 20 Democratic attorneys general challenged the order in court, arguing that it violated several provisions of the Constitution, including the separation of powers, by having the executive branch take control of functions usually regulated by Congress and the states.

The Supreme Court on Monday asked the challengers to respond to the government’s emergency application by Monday, Aug. 3.

Mr. Trump has repeatedly criticized mail-in voting and sought restrictions on it. For years, he has made unfounded claims sowing doubt about voting by mail and claiming that it allows widespread fraud.

So far, federal courts have stymied many of Mr. Trump’s efforts to restrict mail voting.

In late June, a federal judge issued a ruling that blocked key parts of the executive order. Judge Indira Talwani, a federal district judge in Massachusetts, concluded that “the Constitution does not grant the President any specific powers over elections.”

She underlined the words “does not.”

This weekend, a three-judge panel from the U.S. Court of Appeals for the First Circuit upheld her decision.

The judges wrote that if the president’s order were allowed to go into effect for the midterm elections in November, “it would sow confusion and threaten disenfranchisement of many eligible voters.”

The Constitution gives the states and Congress powers over elections, but it does not give those powers to the president, the judges wrote.

The Supreme Court has shown skepticism of Mr. Trump’s efforts to restrict mail-in voting. In late June, the justices upheld a Mississippi law that allows mail-in ballots postmarked by Election Day to be counted if they are received up to five business days later, a rejection of the Trump administration’s efforts to overturn the statute.

In that ruling, Chief Justice John G. Roberts Jr. and Justice Amy Coney Barrett joined the court’s three liberals, announcing that nothing in federal law requires ballots to be received by Election Day provided they are cast by that day. Although the ruling focused on Mississippi’s law, it also appeared to leave in place similar laws in at least 18 other states and territories, including Nevada and California, that harbor battleground congressional districts in the midterm elections.

After the decision was announced, Mr. Trump posted on social media, calling the ruling a “tremendous loss” and urging Congress to pass legislation that places restrictions on mail-in ballots and adds new voter identification requirements.