White House officials said they were pleased by the court’s decision to hear their case, and they expressed optimism that the justices would eventually clear the way for the president’s actions to be carried out.

“The policies will make our communities safer. They will make our economy stronger,” said Brandi Hoffine, an assistant White House press secretary. “They are consistent with the actions taken by presidents of both parties, the laws passed by Congress, and the decisions of the Supreme Court. We are confident that the policies will be upheld as lawful.”

Last February, Judge Andrew S. Hanen of Federal District Court in Brownsville, Tex., entered a preliminary injunction shutting down the program while the legal case proceeded. The government appealed, and on Nov. 9 a divided three-judge panel of the United States Court of Appeals for the Fifth Circuit, in New Orleans, affirmed the injunction.

If the Supreme Court upholds Mr. Obama’s actions, the White House has vowed to move quickly to set up the DAPA program and begin enrolling immigrants before his successor takes over early next year. Democratic presidential candidates have said they would continue the program, but most of the Republicans in the race have vowed to dismantle it and redouble immigration enforcement.

The administration, fearing that the program could remain frozen through the balance of Mr. Obama’s presidency, had asked the court to move quickly. On that point, at least, the court agreed, and it now appears that the case will be argued in April and decided by the end of June.

As is their custom, the justices gave no reasons for agreeing to hear the case, United States v. Texas, No. 15-674.

The new case joins a crowded docket, including cases on abortion, affirmative action, public unions, voting rights and religious liberty. The decisions in all of them will probably land in the late spring and early summer, as the presidential election enters its final stages.