The governor of Russia's Kurgan region on Sunday urged people to evacuate flooded areas immediately, saying rain was exacerbating the already tough situation there and the coming night would be difficult.
The water level in the Tobol river has risen by 25 cm over the past two hours to 5.32 m (17.45 feet), governor Vadim Shumkov wrote on the Telegram messaging app.
"You need to leave while the sun is up," he appealed to local people.
"Gather your families, documents, and valuables and leave beforehand. The situation can worsen sharply at night and you might have not enough time to react."
The Interfax news agency also cited the government of the Tyumen region to the northeast of Kurgan as saying that two villages there were being evacuated as the authorities feared the area could be threatened by the Ishim river.
The TASS news agency cited Russia's emergencies ministry as saying more than 14,000 houses across Russia have been flooded.
In Kazakhstan, also hit by floods, more than 1,000 houses in the city of Petropavlovsk have been flooded, the authorities said on Sunday, with more than 4,500 people evacuated.
Overall, more than 107,000 people have been evacuated in the country since the beginning of the floods.