A Jail official said that at around 2 PM, when Ajay Kumar was walking towards ward number 15, three persons cornered him and stabbed him multiple times with a sharp object.
Police said that there were several injury marks on his face and body, which led to excessive bleeding and could have caused his death.
Kumar had come to the prison last week and was lodged in jail number 4.
His wife Sangeet reportedly told the police that an hour before his death, when she met him at the visitors' meeting point inside the jail, one of the accused had threatened to eliminate Ajay.
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Police said that the three accused-- Sumit, Rakesh and Ramakant alias Raju-- all residents of Tigri extension were known to the deceased.
The three told the police that they were members of the Ravi Gangwal gang. Gangwal, who has several criminal cases against him, is said to be active in Madangir, Ambedkar Nagar and other parts of south east Delhi.
"Ajay had enmity with Ramakant. They used to work together in the past but fell out over some financial issues. Both of them have criminal cases against them. Ajay himself was lodged behind the bars many times in the past.
Till late evening, Delhi Police officers were still inside the prison complex, questioning eyewitnesses in the murder. Police have registered a case and have started the investigation.
Senior jail official said that they are conducting an inquiry into the case and had also informed the police about the incident.