WASHINGTON — President Obama will ask the Supreme Court to clear the way for his far-reaching overhaul of the nation’s immigration system, administration lawyers said Tuesday, setting up a battle in the nation’s highest court over whether nearly five million undocumented immigrants can legally live and work in the United States.

A year after the president asserted the power of his office to provide work permits and protection from deportation for those immigrants, his plan remains under assault by conservatives who have tied it up in legal limbo. On Monday, a federal appeals court said the president had exceeded his authority.

If the Supreme Court agrees to hear the president’s case during the current term, a ruling could come by next summer, just days before the two political parties hold their nominating conventions for the 2016 presidential campaign. A June decision could ensure a fierce debate on an issue that is critical to partisans on both sides.

“This is the moment that we, along with millions of families, have been waiting for,” said Marielena Hincapié, the executive director of the National Immigration Law Center. “We are more than ready to take this case to the Supreme Court.”