The attorneys said Roof's announcement earlier this week that he won't call any witnesses or present evidence to defend himself from the death penalty suggests he lacks the mental capacity to be his own lawyer.
Last month, Gergel ruled that Roof was competent to stand trial. The competency hearing will take place Monday, and Gergel will make the ruling from the bench.
In the penalty phase of a death penalty trial, defendants usually put up witnesses to show the jury why a defendant should get life in prison without parole.
Roof wants to represent himself in the penalty phase of the trial, which the attorneys' request would have delayed.
Lawyers involved with Charleston church shooter Dylann Roof have asked a judge to delay a competency hearing in order to review a mental health evaluation scheduled for this weekend ahead of his sentencing for the massacre previous year. Roof told the judge in Wednesday's hearing that he sees the public release of those documents as problematic.
Commission clears draft expanding Erdogan's power
The changes need to secure the support of at least 330 deputies in the 550-seat assembly before being put to vote in a referendum. It also increases the numbers of lawmakers from 550 to 600 and lowers the age of candidacy for the parliament from 25 to 18.
"In an abundance of caution, the Court orders an additional independent psychiatric evaluation and will hold another competency hearing", Gergel wrote.
Jurors on December 15 found Roof, a 22-year-old avowed white supremacist, guilty of 33 charges of federal hate crimes resulting in death, obstruction of religion and firearms violations stemming from the shooting deaths of nine people attending a Bible study at a historic black church.
Roof's standby counsel made the motion based on "facts developed since the competency hearing held on November 21-22", the order states.
In the order, Gergel announced his appointment of James Ballenger, a Charleston-based forensic psychologist, to conduct a competency evaluation on Roof over the New Year's holiday weekend. Prosecutors say the judge should only provide such an instruction if the jury returns and states it actually is deadlocked. The government also asks the judge to consider adding specific instructions about the role of alternate jurors, particularly since they did not deliberate in the guilt phase of the trial.
Gergel responded that he is still weighing the issue, complicated by a state death penalty trial expected in January, but once proceedings have concluded, the public will likely have a right to know.