In her request for an injunction, Ms. Greene argued that it would be impossible to fully resolve the case before Georgia holds its primary elections on May 24.
Absentee ballots will start to be mailed on April 25, Ms. Greene’s motion said.
In the ruling, Judge Totenberg determined that Ms. Greene had failed to prove that there was a strong likelihood that she would prevail on the merits of her legal claims.
A state administrative judge is scheduled to hear the case on Friday.
The decision by Judge Totenberg stood in stark contrast with a recent ruling in a similar case involving Representative Madison Cawthorn in North Carolina.
In blocking that disqualification effort, U.S. District Judge Richard E. Myers II, an appointee of Mr. Trump, ruled that the 14th Amendment of the Constitution narrowly applied to members of the Confederacy after the Civil War.
They contend that the phrase was a code used to incite violence, and point to the third section of the 14th Amendment in their argument to drop her from the ballot. »