"We will approach the Archaeological Survey of India to rebuild the Rajagopuram in a scientific manner," Rosaiah told reporters here.
Expressing his grief over the incident, he said an inquiry had already been ordered.
"It is a matter which has to be looked into. I don't have any ready made answers," he replied when asked if the negligence by the state's endowments department had led to the collapse.
The government has formed a committee of experts to probe the reasons for the collapse of the ancient tower.
The temple's 45-metre-tall Rajagopuram, which had recently developed cracks, caved in Wednesday night. Police said there was no loss of human life as all shops located near the structure had already been shifted. However, over 100 monkeys are feared dead in the incident.
The Rajagopuram was constructed in 1516 by Srikrishna Devaraya, the ruler of the Vijayanagara empire, to mark his visit to the temple as part of his march across the empire following his victory over his enemies.
On Tuesday, engineers, after an inspection of the seven-storeyed structure, had declared a 150-metre area around it as a danger zone. All shops in the area were then shifted, preventing a disaster.
Srikalahasti temple is among the most visited temples in Andhra Pradesh and is considered a must visit for anyone who visits the famed Tirupati temple.
The cracks had developed in the tower following recent rains. Rosaiah pointed out that few days ago, the government had approached Narasimha Rao, a professor of IIT Madras, to inspect the tower and recommend whether it could be repaired. However, the structure came crashing down even before he could inspect it.