WASHINGTON — The Obama administration said Tuesday it will ask the Supreme Court to reverse a lower court ruling and to back White House efforts to shield more than 4 million immigrants from deportation.

The Justice Department will file an appeal seeking to overturn Monday’s 2-1 ruling by the 5th Circuit Court of Appeals. That decision said Obama had exceeded his authority when he created programs that allowed some immigrants in the country illegally to stay and obtain work permits.

Even if the Supreme Court agrees to hear the high-profile case, they may not rule before Obama leaves office in January 2017. Immigration thus is almost certain to remain a politically contentious issue in the 2016 presidential campaign.

Many Republican candidates have vowed to undo Obama’s immigration orders if they win next November. Democrats have vowed to expand those orders in an appeal to Latinos and others who support easing enforcement of immigration law.

Josh Earnest, the White House spokesman, said the administration will not change its deportation priorities following the court ruling, thus limiting the immediate significance.

With the programs already stalled by the legal battle, he said immigration officials will continue to first deport foreigners with criminal records, those with multiple immigration violations and recent border crossers, not those who applied for work permits.

“The enforcement priorities will remain in place, primarily because it’s just common sense,” Earnest said.

Republican lawmakers hailed the ruling for its rejection of executive power.

“The president simply can’t singly rewrite the country’s immigration laws,” said Sen. Charles E. Grassley, R-Iowa, chairman of the Senate Judiciary Committee. The appeals court ruling mostly stops a program called Deferred Action for Parents of Americans, or DAPA, which was intended to help foreign-born parents of U.S. citizens or permanent residents.

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