The prosecution said the delay stems from the fact that it has not yet decided on the charges it will file against the two suspects, as murder in the first degree may be hard to prove.
The prosecution will instead ask the Ramla Magistrates' Court to remand Rose's grandfather and mother for an additional five days.
Rose, who will be laid to rest on Monday in Paris, France, went missing in May. Her body was found in Tel Aviv's Yarkon River about a week-and-a-half ago after an extensive police canvas, which went on for several weeks.
During a Ramla court hearing on Thursday a police representative said an indictment against Ron and Renault would be filed on Monday, but on Sunday another police official explained the prosecution's predicament.
"If they charge Ron and Renault with murder they will have to prove it was premeditated, and this will be difficult considering the existing evidence," he said, "if they are not indicted for murder, how will the public react?"