A former University of California, Davis, student accused of killing two people and injuring another in stabbings near campus this year is not competent to stand trial, according to the opinion of a court-appointed psychologist presented in court on Tuesday.

The matter of whether Carlos Dominguez is competent to stand trial in the stabbings will now be settled in its own jury trial, because prosecutors contest the psychologist's findings, Yolo County Judge Sam McAdam decided.

The suspect, meanwhile, interrupted Tuesday's hearing on his competency to profess his guilt -- despite his previous not guilty plea in the case.

"I want to apologize and I want to say I'm guilty, and forgive me," Dominguez was heard saying during Tuesday's livestreamed hearing, shortly after McAdam read the psychologist's incompetency finding into the record.

After the interruption, the judge reminded Dominguez of his Fifth Amendment rights. He then briefly suspended the criminal proceedings, adding that anything said during the suspension cannot be used against him.

"Can I have a moment to consult with my client?" public defender Dan Hutchinson quickly asked the judge.

Dominguez had pleaded not guilty to two murder charges and one attempted murder charge through his attorney after his arrest in May.

Authorities have accused Dominguez, who was 21 when he was arrested, of fatally stabbing UC Davis senior Karim Abou Najm and 50-year-old David Breaux in parks near the UC Davis campus in late April, and injuring Kimberlee Guillory in a stabbing near campus in early May.

As for the competency issue: Yolo County District Attorney Jonathan Raven said he disagreed with the psychologist's assessment, prompting the judge to set a jury trial on the competency matter.

Hutchinson noted that it is "extremely unusual" for a competency trial to be heard before a jury and requested a court trial in an attempt to expedite the hearing.

Noting the prosecution's right to a jury trial, which is expected to last about three days, the judge scheduled it for July 24.

Hutchinson declined to comment when contacted by CNN.

The burden rests on the defense to prove incompetence, Raven told CNN in an email.

McAdam scheduled Dominguez to be back in court on July 12 for a status check, and a trial readiness hearing is set for July 19.