About 30 children gathered in a cockpit in the double-decker Bulgaria moments before it sank into the reservoir on the Volga River, a survivor told the Interfax news agency. Russia's Vesti 24 television quoted another survivor as saying that the boat "tilted to the right and sank within minutes."
Crew members had time to open only two lifeboats, and could release only one from the ship, survivors told the Itar Tass news agency.
By early Monday, only two bodies had been recovreed from the 20-meter-deep (66-foot-deep) waters of the giant Kuibyshev reservoir, 3 kilometers (2 miles) from shore.
The regional emergency ministry of Tatarstan said two men managed to swim to shore, while a passing riverboat picked up another 83 people and the lifeless body of a woman. The body of another woman was found later, authorities said without giving details. All aboard were believed to be Russian.
One survivor told Vesti 24 that other ships refused to come to their aid.
"Two ships did not stop, although we waved our hands," said the man in his 40s, who stood on the riverboat amid weeping passengers, some of them wrapped in towels and blankets. He held another man, who was weeping desperately.
Emergency teams and divers from neighboring regions rushed to the site of the tragedy, 450 miles (750 kilometers) east of Moscow.
Throughout the day, officials gave different counts of those on board and the number of missing, but by early Monday officials in Moscow and Tatarstan agreed that the boat had held 150 passengers and 38 crew members when it got into trouble.
The Volga, Europe's longest river, is up to 30 kilometers (19 miles) wide. The river is a popular tourist destination, especially in summer months. Most of Russia's largest cities are located in the Volga River basin.
The Bulgaria was built in 1955 in Czechoslovakia and belongs to a local tourism company. It was traveling from the town of Bulgar to the regional capital, Kazan.
A tourism expert said the lack of partitions inside the Bulgaria made it vulnerable to breaches.
"It case of an accident these ships sink within minutes," Dmitri Voropayev, head of the Samara Travel company, told the Ria Novosti news agency.
Russia's Union of Tourism Industry said the ship had not been inspected and retrofitted for years, according to the Interfax news agency.