The official Xinhua News Agency said four cars on the second train also derailed, but it did not say how serious that was.
The first train was traveling from the Zhejiang provincial capital of Hangzhou when the accident occurred in Wenzhou city at about 8:30 p.m. (1230 GMT), Xinhua said.
One carriage from the first train fell about 65 to 100 feet (20 to 30 meters) from an elevated section of track, Xinhua said. Pictures on the Internet showed one badly damaged car lying on its side by the bridge and the second car leaning against the bridge after landing on its end.
Xinhua quoted an unidentified witness as saying "rescuers have dragged many passengers out of the coach that fell on the ground."
Xinhua earlier has reported that at least 89 people were injured in the collision. The news agency did not give a new figure for the number of injured after reporting that the death toll had been raised to 32.
The trains involved are "D" trains, the first generation bullet train with an average speed of about 95 miles (150 kilometers) per hour and not as fast as the new Beijing-Shanghai line.
Xinhua said the train hit by lightning was "D3115." It said the Ministry of Railways confirmed that it was hit from behind by train "D301."
China has spent billions of dollars and plans more massive spending to link the country with a high-speed rail network. Recently, power outages and other malfunctions have plagued the showcase high-speed line between Beijing and Shanghai since it opened on June 30.
Official plans call for China's bullet train network to expand to 8,000 miles (13,000 kilometers) of track this year and 10,000 miles (16,000 kilometers) by 2020.
The huge spending connected with the rail expansion also has been blamed for corruption, and Railways Minister Liu Zhijun was dismissed this spring amid an investigation into unspecified corruption allegations.
No details have been released about the allegations against him, but news reports say they include kickbacks, bribes, illegal contracts and sexual liaisons.