The court's 4-4 tie ruling on June 23 effectively kept in place the lower court ruling blocking the Obama plan.
The Justice Department wants the order to be kept on hold until a ninth justice is confirmed. Obama has nominated Judge Merrick Garland to fill the seat of Justice Antonin Scalia, who died suddenly in February, but the Republican Senate has not agreed to a hearing or vote on Garland.
The Supreme Court will not act on the request until at least October, when the new term begins. The presidential election to succeed Obama is Nov. 8.
Acting Solicitor General Ian Heath Gershengorn acknowledged in the filing Monday it's a long shot and "exceedingly rare for this court to grant rehearing." It said the last time the request was granted was in 1954.
The Justice Department said the move "is consistent with historical practice and reflects the need for prompt and definitive resolution of this important case."
The president's executive order announced in April 2014 a plan to shield more than 4 million people from deportation. Twenty-five states joined Texas in a suit that claimed the president didn't have the power to order the changes.
Obama's plan would shield undocumented immigrants living in the United States for several years without committing serious crimes and with family ties to those in the U.S. legally.