A federal appeals court refused to lift an injunction against President Obama’s deportation amnesty in a ruling Tuesday that delivers a second major legal setback to the administration and keeps millions of illegal immigrants on hold.

The U.S. Court of Appeals for the Fifth Circuit sided with a lower court that ruled Mr. Obama probably broke the law in taking unilateral action last year to grant an amnesty from deportation. The three-judge panel, ruling 2-1, shot down Mr. Obama’s hopes of quickly restarting the amnesty, and make it likely he’ll have to go to the Supreme Court to try to win his case.

The majority, Judges Jerry E. Smith and Jennifer Elrod, said the president’s new program, known as Deferred Action for Parental Accountability, or DAPA, is a binding policy that should have gone through the usual public notice and comment period instead of being announced unilaterally by Mr. Obama and Homeland Security Secretary Jeh Johnson late last year.

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“We live in a nation governed by a system of checks and balances, and the president’s attempt to bypass the will of the American people was successfully checked again today,” said Texas Gov. Greg Abbott, who, as his state’s attorney general last year, began the lawsuit challenging the new amnesty.

Twenty-five states joined Texas in suing to halt the amnesty, arguing they would bear new costs in having to issue driver’s licenses to the illegal immigrants and provide health care and other services to them. The states said the president’s actions were unconstitutional or, at the very least, illegal.

First a district court, and now a federal appeals court, have sided with Texas, serving as twin legal rebukes to Mr. Obama and his defenders, who had insisted the steps he took were consistent with the law and with previous presidents’ actions.

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Immigrant rights advocates said they will keep fighting, and tried to cast both the district and appeals courts as legal outliers.

“We are on the right side of history, the right side of justice,” said Marielena Hincapie, executive director of the National Immigration Law Center.

The rulings do not affect Mr. Obama’s 2012 amnesty for so-called Dreamers, which has already granted tentative legal status to more than 600,000 illegal immigrants, and it also doesn’t take away Mr. Obama’s ability to decline to deport illegal immigrants. That means none of the more than 4 million people in question are likely to be kicked out of the country.

But the judges have ruled that Mr. Obama can’t go further and grant many of those people an affirmative status carrying all sorts of benefits, including driver’s licenses, tax credits and preferential work status under the terms of Obamacare.

Immigrant rights advocates challenged Mr. Obama to use his authority to halt all deportations until he can find a way to work with Congress on a new immigration law.

“We call on President Obama to immediately act on that power by halting all deportations until the day when our broken immigration system can be replaced by humane, rational policies that recognize the value and humanity of our immigrant community members,” said Jessica Bansal, litigation director for the National Day Laborer Organizing Network.

The judges’ rulings hinged in large part on the findings of District Judge Andrew S. Hanen, who halted the program in February, just two days before it was to accept the first applications.

Judge Hanen ruled that an earlier version of the amnesty, which Mr. Obama announced in 2012 and which applied to so-called young adult Dreamers, showed that the administration was approving most applications. Judge Hanen said that undercut Mr. Obama’s argument that he was showing discretion rather than issuing a binding policy.

The judges in the majority opinion Tuesday said Mr. Obama’s expansion appeared to be the same kind of policy, and would have serious effects on the states.

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