According to local media, two women and a man are dead.
Six people are still reported to be trapped in the cave.
A total of 26 rescue workers participated in the exercise, and several could be rescued at an early stage.
Police and ambulance personnel are on site to assist the rescue service to rescue those who are still in the cave but the work is hampered by heavy rain.
Altinopolis is known for its caves, which are a major tourist attraction.