President Xi Jinping has called for an all-out rescue effort.
Premier Li, Vice-Premier Ma Kai and State Councilor Yang Jing arrived at the rescue site.
Li demanded that all government agencies, especially the Ministry of Transport, quickly contribute resources for the rescue work.
Li stressed that local governments in the area should prepare to deal with the aftermath of the disaster, and he demanded that officials conduct an investigation into the cause of the disaster. He later visited survivors in a local hospital.
Among the survivors were the ship's captain and chief engineer, who were in police custody for possible questioning.
According to Xinhua News Agency, they claimed the ship was hit by a tornado and tipped over in as little as one minute.
The China Meteorological Administration confirmed on Tuesday that there had been a tornado in the area.
Xinhua said the ship was not overloaded, and that it was equipped with enough life jackets.
More than 3,000 people are participating in the rescue. The Chinese People's Liberation Army navy sent more than180 divers to the site.
Near Erjitou, about 30 minutes by boat from the site, at least 70 members of a pontoon bridge troop from Wuhan, Hubei province, were waiting for orders.
The troops left Wuhan at around 7 am on Tuesday in a convoy of 20 trucks carrying assault boats, according to Su Junjie, a publicity officer of the unit.
By 6:30 pm, Su said, they were still waiting for their turn to offer help as other rescuers had been diving to search for survivors and were trying to turn the vessel upright.
The search and rescue operation had been made difficult by lingering rain throughout Tuesday.
Liu Yang, who lives near Erjitou, said heavy rain began to hit the area at around 7 pm on Monday. It peaked at around 9 pm, with thunder and lightning strong enough to smash windows and cause a power outage to much of his community.
"We have never seen such bad weather," the 35-year-old said. "And I have never heard of an accident more disastrous than the one last night."
The Guangdong Maritime Safety Administration has launched a safety inspection of passenger vessels, ferries and hazardous goods vessels across the province.
In the monthlong campaign, which started on Tuesday, workers in the sector will be trained on safety issues, review emergency programs, take emergency drills and eliminate flaws in safety management.
The administration will conduct a thorough check of the weather alert issuing system.
June marks the start of the tourism season in China and is part of the storm season featuring high temperatures and frequent rain storms.
