On the first day the panel obtained details of the investigation carried out by the Special Investigation Team (SIT) constituted by the Telangana government.
Rachakonda Police Commissioner Mahesh Bhagwat, who headed the SIT, met the three-member judicial commission to apprise it of its findings.
Headed by a former Supreme Court judge, Justice V.S. Sirpurkar, the commission also has former judge of Bombay High Court Justice Rekha Sundar Baldota and former CBI director D.R. Karthikeyan as members.
It is conducting its hearing at the premises of Telangana High Court. The Central Reserve Police Force (CRPF) is providing security to the panel.
Over the next two days, the commission is likely to examine officials of Cyberabad Police including those who took part in the alleged encounter.
The panel is also likely to gather details from forensic experts who conducted the autopsy of the bodies of the four accused. It will also record the statements of the families of the four men.
Two truck drivers and two cleaners, all aged between 20 and 26 years, were shot dead by police at Chatanpally near Shadnagar town, about 50 km from Hyderabad, on December 6.
Police claimed that the accused who were taken to the crime scene to make some recoveries, attacked police personnel and even snatched their weapons and fired. It said all four were killed when police returned fire.
All the four were accused in the brutal gang-rape and murder of the 26-year-old veterinarian at Shamshabad on the outskirts of Hyderabad on November 27.
According to police, after the sexual assault and murder, the accused shifted the victim's body to Chatanpally where they set it afire.
The alleged encounter was hailed by those demanding immediate justice to the victim but human rights groups raised doubts about the police claim and approached the Supreme Court for a thorough probe.
The Supreme Court on December 12 appointed the three-member commission, directing it to submit its report within six months from the date of its first sitting.
A bench of Chief Justice S.A. Bobde, Justice Abdul Nazeer and Justice Sanjeev Khanna barred the Telangana High Court and the National Human Rights Commission from initiating or proceeding with any probe already initiated into the encounter.
( With inputs from IANS )