Esther and Jean-Claude Morel had hoped the trial would bring them closure following the murder of Adeline in 2013, Blick reported.
“This is torture for us. We want it to be over so we can start the grieving process. Now it is going to be months before it resumes,” Esther Morel told the paper. “We had prepared for this day.”
The trial of Fabrice Anthamatten, 42, began in Geneva on Monday and was scheduled to last two weeks.
But the proceedings were abruptly halted on Thursday after the two judges called for a third psychiatric report.
The trial is not now expected to resume for another six months.
The judges were unhappy after it emerged that one of two French experts called to give evidence on Anthamatten's mental state had only seen his file on the day they met the suspect.
The presiding judge said the court had the impression that the two experts had not studied all the relevant material.
The two French experts have special knowledge of serial killers. Testifying on Wednesday, they said they believed there was a high risk of Anthamatten reoffending.
The court is now looking for a third expert to present testimony.
The defendant admits killing his therapist in September 2013 during day-release from his detention centre.