The request is scheduled to be argued Tuesday in the U.S. District Court for the Southern District of New York, with the NFLPA asking for a ruling before 4 p.m. ET.
The move comes as the Cowboys, coming off their bye week, prepare to return to practice Tuesday before next Sunday's game at San Francisco. The NFLPA notes in its filing that the NFL on Monday informed the Cowboys that Elliott will not be permitted to participate in that game or this week's practices.
A federal appeals court last Thursday lifted an injunction that blocked Elliott's six-game suspension, clearing the way for the NFL's punishment over domestic violence allegations.
That ruling, by the 5th U.S. Circuit Court of Appeals in New Orleans, reversed the order last month of a federal judge in Texas.
That judge had issued an injunction that blocked the suspension, agreeing with NFL players' union attorneys who argued that the investigation of the allegations in Ohio and subsequent appeal were unfair to Elliott.
The NFLPA said after last Thursday's ruling that it will request an en banc hearing -- a hearing of the full panel of judges within the 5th U.S. Circuit Court of Appeals in New Orleans -- on behalf of Elliott.
The Monday filing by the NFLPA seeking a restraining order asserts that the decision by the appeals court was made based on a matter of jurisdiction while not analyzing the merits. The filing goes on to say that "the Eastern District of Texas has already held [twice] that Elliott will suffer irreparable harm from a suspension," and adds that "the NFL's rejoinder that Elliott will not suffer severe and irreparable harm to his season, career, and reputation as a result of his six-game suspension -- nearly half of an NFL season -- defies reason in this industry, where players' careers are precarious and short."
Material from The Associated Press was used in this report.