Rescuers were still cutting open the mangled wreckage to free several passengers trapped, hours after the crash at Warangal, about 145 km northeast of the Andhra Pradesh state capital Hyderabad.
"The situation is very bad," local district police chief Nalin Prabhat said.
The Guntur-Hyderabad Golconda Express was nearing Warangal station when the engine and two coaches jumped the tracks at about 10:30 am (0500 GMT) and fell on to a road below, crushing vehicles and pedestrians.
Nine passengers and six people on the road were killed.
"Five of the bodies are still trapped under the engine. We are making efforts to retrieve them," Prabhat said.
In India’s capital New Delhi, chief railways spokesman M Siddiqui said the accident occurred when the Express, travelling from Guntur town applied emergency brakes after missing a red signal.
Wednesday's crash came less than two weeks after 51 people died in western India when a train crashed into a tunnel entrance blocked by boulders that had fallen in a landslide.
India has one of the world's largest railway networks, with almost 14,000 trains carrying more than 13 million passengers a day. But its safety record is poor, with about 300 accidents a year.