Several districts of the northern Kazakh city of Petropavlovsk were completely flooded and cordoned off on Monday, a Reuters witness reported from the city.
Some residents of the city of more than 200,000 said their houses had been submerged up to their roofs or even got detached from their foundations and floated away.
The Tobol, a tributary of the Irtysh, rose 23 cm (9 inches) in the four hours to 6 a.m. (0100 GMT) on Monday, regional authorities said.
Floods were also inundating homes in the Tomsk region in the southwestern part of Siberia, regional officials said on Telegram.
Almost 140 houses near the city of Tomsk, which is the regional administrative centre, were under water on Monday and 84 people were evacuated.
Almost 5,000 houses remain flooded, a ministry spokesman told a briefing, although nearly 12,000 people have returned to their homes.
Cars move through a flooded part of a road in the city of Petropavl in Kazakhstan on Sunday. AFP
Earlier, 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.
A view of a temporary housing for those evacuated from flood-hit areas of city of Petropavl in Kazakhstan. AFP
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 111,000 people have been evacuated in the country since the beginning of the floods.
Reuters