AUSTIN, Texas—The Obama administration on Monday asked a Texas federal judge to allow it to continue implementing the president’s immigration plan, arguing that the judge had veered from established immigration law by blocking the plan last week.

The emergency request by the Justice Department asked U.S. District Judge Andrew Hanen to render a decision by Wednesday, saying that otherwise, it may ask the Fifth U.S. Circuit Court of Appeals in New Orleans to quickly block the order.

The stay, if granted, would allow the administration to continue laying the groundwork for its Deferred Action for Parents of Americans and Lawful Permanent Residents program, which would permit about four million people in the country illegally to apply for deferred deportation and work authorizations.

A stay also would allow the administration to begin a planned expansion of the 2012 program called Deferred Action for Childhood Arrivals, known as DACA, which allows relief for people brought to the U.S. as children.

On Feb. 16, Judge Hanen blocked the administration from proceeding with the plans, which Mr. Obama announced in November, siding with Texas and officials from 25 other largely Republican states who had sued, alleging they represented an unconstitutional overreach of presidential power.

Twelve other mostly Democratic states, as well as mayors from more than 30 cities including Los Angeles and New York, have filed briefs supporting the administration.

The Obama administration on Monday filed a separate appeal of the injunction to the Fifth U.S. Circuit Court of Appeals in New Orleans. The fight quickly could move to the U.S. Supreme Court.

In the brief requesting a stay, the federal government gave a glimpse into the arguments it plans to make to counter the states’ case. It contested the states’ standing to challenge policy decisions it says exclusively belong to the executive branch.

It also argued that Judge Hanen, at a minimum, should allow the administration to continue implementing the immigration program outside of Texas, because his ruling detailed only the harm Texas would suffer if the program was instituted.

The judge found that Texas would incur costs for processing driver’s licenses for individuals benefiting from the program.

The government also argued that blocking the program’s implementation would frustrate “a comprehensive and integrated effort…to prioritize immigration enforcement efforts,” while costing federal taxpayers the salaries, rent and other expenses already set aside to process applications.

The harm to federal interests, the administration said, far outweighed any Texas could claim.

Texas Attorney General Ken Paxton, who is leading the suit by the states, said Monday it would press its challenge.

“The attempts by the Obama administration to circumvent Congress and change federal immigration law by executive action were properly stayed by a federal court,” he said.