It has been a major impediment to President Trump’s agenda — the ability of a single federal judge in a single district to block a policy across the country.

On issue after issue, the White House has been stopped by judges from carrying out Mr. Trump’s initiatives while they are litigated in court, including his ability to withhold funds from schools with diversity programs, to relocate transgender women in federal prisons and to remove deportation protections from hundreds of thousands of Venezuelan migrants.

On Thursday, the Supreme Court will take up one such case, with potentially major implications for the power of the judicial branch.

The dispute stems from an executive order signed by Mr. Trump on the first day of his second term that ended the practice of granting citizenship to all children born in the United States. The policy was blocked almost immediately by federal judges who ruled that it was unconstitutional.

The debate over whether such freezes are legal has simmered for years, as district court judges have issued orders blocking the actions of presidents from both parties. But Mr. Trump has expressed particular outrage about them since he returned to office. Some of the justices have also been critical of nationwide injunctions.

A decision that limits nationwide injunctions could dramatically reshape how federal courts handle challenges to Mr. Trump’s policies, curbing the power of federal judges to swiftly block policies and boosting executive power. Groups opposing Mr. Trump’s actions would most likely have to bring many individual claims, or pursue other legal pathways, such as class action lawsuits.

Should the Trump administration sway the justices, the immediate implications for Mr. Trump’s executive action ending birthright citizenship would not be entirely clear. The groups that have challenged the order have warned of chaos, with birthright citizenship potentially ending in some states but not others.

Trump administration lawyers have argued that those fears are overblown, and that nationwide injunctions have prevented the executive branch from even preparing to carry out Mr. Trump’s orders by writing or issuing guidance about how a policy might work.

Although the justices are not expected to immediately weigh in on Thursday on the constitutionality of Mr. Trump’s birthright citizenship order, the oral argument may provide hints of where they stand.

While the justices have issued written orders in response to emergency applications that arose from other Trump administration actions, Thursday’s case marks the first time since Mr. Trump returned to office that the Supreme Court will hear an oral argument stemming from one of his policies.

The argument will take place after the justices have heard all of their scheduled cases this term, and in the weeks before they begin issuing their most consequential decisions of the year — an unusual move that signals that the justices regard the dispute as significant enough to consider immediately.

Birthright citizenship, or the practice of granting citizenship to people born in the United States to parents who are not citizens, has long been considered a tenet of immigration law. The 14th Amendment, ratified after the Civil War, declared that “all persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside.”

In 1898, the Supreme Court affirmed that right in a landmark case, United States v. Wong Kim Ark. For more than a century, courts have upheld that constitutional interpretation.

Mr. Trump’s executive order drew immediate legal challenges from 22 Democratic-led states, and from immigrant advocacy groups and several pregnant women who contested the order, saying they feared their children would be denied U.S. citizenship. Federal judges in three states quickly paused the policy while court challenges continued. On March 13, the Trump administration asked the justices to step in and lift the court-ordered blocks, which most likely would have allowed the policy to go into effect in the states that had not sued.

More than a month later, on April 17, the justices announced that they would schedule an oral argument to consider the legality of the nationwide injunction.

The Supreme Court has never ruled directly on the issue before, in part because judges have used nationwide injunctions far more frequently in recent years.

Some justices have signaled opposition to their use. In a 2020 decision, Justice Neil M. Gorsuch criticized injunctions of “‘nationwide,’ ‘universal’ or ‘cosmic’ scope,” writing that such “patently unworkable” rulings were “sowing chaos.” Justice Samuel A. Alito Jr. has also criticized nationwide blocks.

In a legal brief, the immigrant groups challenging the birthright order argued that the justices do not need to issue such a ruling now, because “case-specific considerations” support such nationwide freezes.

They cite the judiciary’s power under Article III of the Constitution to issue such rulings. And they argue that if judges had been barred from making rulings that applied to parties not directly involved in litigation, courts could not have outlawed school segregation or racial gerrymandering.

Thursday’s argument consolidates three challenges to the Trump executive order imposed by federal courts in Maryland, Massachusetts and Washington State.

Judges in each state have been skeptical of Mr. Trump’s attempt to end birthright citizenship. At a hearing in Seattle, Judge John C. Coughenour, a Ronald Reagan appointee, said: “I’ve been on the bench for over four decades. I can’t remember another case where the question presented is as clear as this one. This is a blatantly unconstitutional order.”

In their emergency application to the justices, Trump administration lawyers argued that any order issued by the those trial judges should have only applied to parties directly involved in the court challenges.

Sarah M. Harris, the acting solicitor general at the time, called the government’s request a “modest” one, an effort to limit the freeze on the policy to “parties actually within the courts’ power.”

Immigrant groups and leaders of the 22 Democratic-led states argued that the birthright citizenship case showed why nationwide injunctions were a necessary tool.

“There is nothing ‘modest’ about the government’s request for emergency relief in this case,” two immigrants’ rights groups — CASA Inc. and the Asylum Seeker Advocacy Project — argued in their own filing.

It is not clear how much the justices will engage with the substance of Mr. Trump’s executive order. But Matthew J. Platkin, New Jersey’s attorney general, said he thought the justices would need to wrestle with the practical consequences of the policy.

“Clearly there are going to be some justices who want to talk about the merits,” he said in an interview Wednesday. “I don’t know how you consider a nationwide injunction in this case without considering the merits.”

Mr. Trump has said he would welcome it.

In comments to reporters in the Oval Office after the justices announced they would hear oral argument, Mr. Trump had said that he was “so happy” the court agreed to hear the case.