Witnesses said the bus was apparently speeding when it spun off the road and into the Kelkit River near Resadiye, in Tokat province, about 330 kilometres northeast of Ankara.
Eleven people survived the pre-dawn accident.
About 45 people were believed to have been aboard the bus en route from Istanbul to Van, eastern Turkey, a trip of more than 1,600 kilometres.
Hopes of finding survivors faded in the afternoon as divers recovered all the bodies trapped inside the bus and continued their search downstream.
Officials said they expect the death toll to rise.
Brazil bus
Meanwhile at least 14 people died when their bus veered over a cliff near the southeast Brazilian city of Uberlandia, in Minas Gerais state.
Twenty-six people were rushed to a local hospital after the accident.
Some passengers said the crash happend as the driver tried to change a music track on the vehicle's sound system.
The bus was carrying 40 passengers and was en route to a resort in central Brazil.
It is unclear if the driver died in the accident or was among the injured.