“The executive branch is bound by our legal system and U.S. Constitution — it cannot simply create new laws unilaterally,” Attorney General Ken Paxton of Texas said in a statement after the hearing.

If the government lawyers fail in their bid to reverse the judge’s preliminary injunction, Mr. Obama’s immigration efforts could remain in legal limbo for months, raising doubts about whether the policies will be carried out before the president leaves office.

The hearing before the three-judge panel allowed lawyers for both sides to make their cases publicly. In most similar cases, legal experts said, appeals courts make decisions based solely on written briefs. In this high-profile case, however, each side had one hour to argue — twice the amount of time generally provided to lawyers in Supreme Court cases.