Shoot us, but don't send us back to Tihar Jail, they said in court, according to their lawyers.
Their request was turned down, but the judge has asked jail officials to submit a daily report on the security arrangements for the suspects.
Mr Singh, 35, was discovered dead at 5 am in a cell he shared with three other prisoners, none of them linked to the Delhi gang-rape case. (Read: Foreign media on Ram Singh's death) Jail officials cannot explain how his cellmates slept through his alleged suicide, which was also not detected by a guard posted to monitor the cell because Mr Singh was on "a suicide watch." (Read)
They say he tied his shirt to threads from a mat in his jail, and then used a bucket to fasten the rope he had created to the ceiling grille. (Read)
His family says he has been killed. "He couldn't have committed suicide with just one hand," said Ram Singh's father. (Read)
The police say that on the night of December 16, the six suspects, led by Mr Singh, headed out on the school bus he used to drive by day.
They allegedly picked up a 23-year-old physiotherapy trainee and her male friend, assaulted them both with an iron rod, took turns raping the student, then threw the couple onto the road. The woman died in hospital two weeks later. The barbarous attack on her triggered huge protests and a call for urgent, new anti-rape laws, introduced by the government last month.
All six suspects have pleaded not guilty to rape and murder charges. One of them, who is 17, is being tried by a juvenile court.