Many clues were found during last 24 hours, the minister told reporters and exuded confidence that the case would be cracked soon and the culprits would be arrested.
She said the government would take all steps to ensure that the guilty are punished as early as possible.
The home minister said Hyderabad and Cyberabad police commissioners had formed 15 teams, each comprising 10 to 15 officers, to investigate the terror attacks.
The Crime Investigation Department (CID) is also conducting a probe while National Investigating Agency (NIA) and other central agencies are also assisting the state.
Sabita Indra Reddy said terrorists had been trying to carry out attacks since 1995. "They tried at least 20 times. Unfortunately there were more casualties in Lumbini Park and this time in Dilsukhnagar."
Chief Minister N.Kiran Kumar Reddy, who reviewed the law and order situation with home minister and top police officials, directed them to take all steps to prevent more terrorist attacks.
As part of the steps to strengthen the security in the state capital, 3,500 CCTV cameras would be installed in Hyderabad and Cyberabad police commissionerate limits over next six months. The chief minister has approved this plan, which will cost Rs.450 crore.
The government also plans to amend building regulations to make it compulsory for new buildings to install CCTV cameras.
The home minister said 15 out of 16 bodies of the victims were handed over to their families.The injured are undergoing treatment in six hospitals and the condition of six of them is critical.
The chief minister also reviewed with the officials of health department the medical aid being given to the injured. He directed them to ensure that the injured get best treatment. The government will bear the total cost of the treatment.