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Writing for the majority, Justice Anthony M. Kennedy specifically backed last year’s Morton memo as a key part of the federal system.

“The federal statutory structure instructs when it is appropriate to arrest an alien during the removal process. For example, the attorney general can exercise discretion to issue a warrant for an alien’s arrest and detention ‘pending a decision on whether the alien is to be removed from the United States,’” Justice Kennedy wrote.

Even in dissent, Justice Antonin Scalia seemed to accept Mr. Obama’s wide discretion, though he took the unusual step of specifically criticizing Mr. Obama’s categorical exemption two weeks ago for younger illegal immigrants.

“Thousands of Arizona’s estimated 400,000 illegal immigrants — including not just children but men and women under 30 — are now assured immunity from enforcement, and will be able to compete openly with Arizona citizens for employment,” Justice Scalia said.

That may not be enough for some advocates, who said they want to see an even broader exemption for older illegal immigrants.

At a panel discussion at the National Association of Latino Elected and Appointed Officials’ annual conference last week, the White House’s senior immigration policy adviser, Felicia Escobar, was peppered with questions about the need for a better policy to halt deportations.

Advocates said too many immigrants without criminal records are being deported under the administration’s priorities.

From the right, Mr. Aguilar, executive director of the Washington-based Latino Partnership for Conservative Principles, said the court’s decisions validate what Mr. Obama did earlier this month — but also open the door for him to do even more on a unilateral basis.

“If the president really believes in legalization, he probably has the authority on deportation,” Mr. Aguilar said. “He could actually issue an order basically saying, on his discretion, those who have no criminal record will not be deported — period.”