WASHINGTON — The Obama administration appealed to the Supreme Court Friday to rescue its plans to shield from deportation millions of immigrants who are in the country illegally.

Moving quickly to put the issue before the justices in time for a decision while President Obama is still in office, the administration called for the court’s immediate review of its plan to protect and give work permits to as many as 5 million immigrants. The immigrants affected are mainly parents of U.S. citizens and lawful permanent residents.

The appeal, filed exactly a year after Obama announced his executive actions on immigration, injects the Supreme Court into a dispute between 26 mainly Republican-led states and the Democratic administration, amid a presidential race in which immigration has been a flashpoint. So far, the federal courts have sided with the GOP-led states and effectively blocked the plan.

But time is running short for consideration of the immigration issue in the court’s current term. Texas, the lead state in the lawsuit, has 30 days to respond but could ask for more time.

If the justices don’t agree by mid-January to hear the case, the issue probably will not be decided until after Obama leaves office in January 2017.

At issue is the Deferred Action for Parents of Americans program, which Obama said would allow people who have been in the United States more than five years and who have children who are in the country legally to “come out of the shadows and get right with the law.”

An earlier program that is not being challenged, Deferred Action for Childhood Arrivals, shields immigrants brought to the country illegally as children. More than 720,000 young immigrants have been granted permission under that program to live and work legally in the United States.