Kohberger is accused of killing four University of Idaho students in their off-campus home in 2022.
This defense requested to move the case out of town, saying in a recent memorandum he can't receive a fair trial in Latah County because of "inflammatory" publicity.
Kohberger's lawyers are citing a survey they conducted of potential jurors.
However, prosecutors rejected that argument in a filing, saying the court could put in place other measures to ensure a fair trial.
On March 22, Judge halted the surveys being conducted by the defense team, leading to discussions on the matter during hearings on April 4 and April 10, but it was later allowed to continue "without modification."
The judge ruled that most of the survey questions were not in violation of the court's non-dissemination order in the case. Many of the questions included in the defense surveys came from the probable cause affidavit that was not sealed in the case, the judge argued.
The filings are the latest pre-trial developments in Kohberger's quadruple murder trial, which is set to begin in June 2025.
It's been a long and winding road since the four students - Kaylee Goncalves, Ethan Chapin, Xana Kernodle and Madison Mogen - were fatally stabbed in the overnight hours of November 13, 2022, at a home just off the school's main campus in Moscow, Idaho.
Kohberger, a Washington State University graduate student in criminology, was arrested in the killings on December 30, 2022, in his home state of Pennsylvania. A not-guilty plea was entered on his behalf in May 2023, and his attorneys have indicated the 29-year-old intends to present an alibi as part of his defense. Prosecutors have said they will seek the death penalty.
The progression of the case has been slowed by a series of pre-trial motions and hearings that have frustrated the family of one of the victims as well as the judge overseeing the case.
The hearings largely fall into a few different buckets. One relates to the defense attorneys' access to evidence, particularly how the prosecution used investigative genetic genealogy in building the case. A second set of hearings concerns Kohberger's proposed alibi for his innocence. Third, there have been a number of hearings related to a gag order that restricts what the parties can publicly say about the case.
ABC News contributed to this report.