Ramzan Rizwan, 25, made the request when he appeared via video-link with Rasheed Muhammad, 43, at the third hearing of his case in a district court yesterday.
Ramzan told District Judge Eddy Tham that he could not tolerate the conditions in his cell, saying it was "too extreme."
"Either you send me to the gallows or send me back to my country," The Straits Times quoted Ramzan as having told the court.
When Ramzan requested again to be sent back to jail in his country, the judge told him he had no power to give such an order.
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The prosecution applied for Ramzan to be remanded for further psychiatric assessment.
Rasheed, the other accused whose psychiatric assessment has been done, said whatever had happened was wrong.
"It is my wrongdoing," he told the judge.
Rasheed was emotional when he talked about his eight children - six girls and two boys - all of whom are not working, according to the Singapore daily.
The victim's legless body was found in a blood-soaked suitcase. Police later found the legs from a Muslim cemetery.
All three were reportedly from the same village in Pakistan and had come to Singapore in May to sell tissue papers.