Reddy said there were more than 70 people on the crowded boat when it sank 100 metres from the bank in deep water.
"So far we have recovered the bodies of 13 people including a woman and two children," he said. Some of the younger passengers swam to safety, but the elderly and many women and children were among the missing, he said.
Authorities said divers found a further nine bodies, including those of two women and four children, late on Friday.
A survivor told Reuters by telephone that he swam to safety along with his 12-year-old son but lost his daughter and wife.
"I watched helplessly as my wife and daughter drowned a few metres away," the man, who gave his name as Maddisetti, said from a government hospital in Kollapur, a nearby town.
He said the boat was so crowded that passengers had to grab hold of each other to prevent people falling overboard.