Early this month, one of the accused was found dead in Delhi's main Tihar Jail.
K. Girdhar said there had been 20 suicides at Tihar Jail between 2001 and April 2012.
Guru, who had been on death row since 2002, was executed at Tihar jail in Delhi.
BBC: Afzal Guru hanging: Fourth day of curfew in Kashmir Valley
He had been on death row since 2002 and was executed at Tihar jail in Delhi.
Mr. Gupta, the Tihar Jail spokesman, said the prisoners in the rape case had been treated properly.
Tihar Jail is badly overcrowded with nearly twice as many prisoners as it was designed to hold.
Times Now is repeatedly running "Security Lapse at Tihar Jail" as its headline.
On Monday, one of the five men accused in the rape was found dead in New Delhi's Tihar jail.
Tihar Jail spokesman Sunil Gupta separately said authorities there were "keeping a close eye" on the four surviving defendants.
On Monday, one of the five men accused in the rape incident was found dead in Delhi's Tihar jail.
The family of Mr. Guru, which resides in north Kashmir, was informed about his hanging by Tihar Jail authorities.
One of the suspects, Ram Singh, was found dead in his shared cell at Delhi's Tihar jail earlier this month.
Mr. Guru was executed on Feb. 9 in New Delhi's Tihar Jail, and was buried inside the prison shortly after.
Officials said Mohammed Afzal Guru, who had been on death row since 2002, was executed at Tihar jail near Delhi.
Mr. Anand, the lawyer for the Singh brothers, said Mukesh, the surviving brother, claimed to have been tortured by police in Tihar Jail.
Lawyers for all the defendants, who are in custody in Delhi's Tihar jail, say their clients are innocent and will enter not-guilty pleas.
K. Anand, the lawyer for the Singh brothers, said Mukesh, the surviving brother, claimed to have been tortured by police in Tihar Jail.
Aaj Tak says "Delhi gang-rape suspect's death creates doubts over jail's security", and ABP News channel says "Singh's suicide exposes Tihar jail's lax security".
And in February, a Kashmiri man, Afzal Guru, was sentenced to death for the 2001 attack on India's parliament, was hanged in Delhi's Tihar jail.
Tihar Jail embraced a series of reforms in the 1990s and today boasts child-care facilities, meditation and yoga programs, music classes and skill-building training projects.
The Ministry of Home Affairs has sought a report from Tihar Jail authorities on the suicide, a senior ministry official told The Wall Street Journal.
The family of Guru, who were not informed before he was executed, have rejected the Indian government's offer to visit his grave in Tihar jail.
BBC: Afzal Guru hanging: Fourth day of curfew in Kashmir Valley
The body of Mr. Guru, who has been on death row for more than 10 years, was buried in Tihar Jail, local television channels said.
Most Indian news TV channels and websites are giving wall-to-wall coverage of the death of Delhi gang rape accused Ram Singh in the capital's Tihar jail.
Singh, said his clients feared for their safety at the prison, Tihar Jail, and that he was planning an appeal for them to be moved elsewhere.
Singh, the lawyer for two of the defendants, said one of his clients, Akshay Thakur, asked him in court to keep him out of Tihar Jail.
Mr. Gupta, the Tihar Jail spokesman, said the prisoners in the rape case have been treated properly and confirmed that authorities believe Mr. Singh committed suicide.
Tihar Jail embraced a series of reforms in the 1990s and today boasts childcare facilities, meditation and yoga programs, music classes and other skill-building training projects.
Ram Singh, 33 years old, was found dead in his cell at Tihar Jail early Monday in what police and prison authorities said was suicide by hanging.
Mr. Singh, the lawyer for two of the accused men, said one of his clients, Akshay Thakur, asked him in court to keep him out of Tihar Jail.
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