Tens of thousands of people have fled their homes as several months of rain fell in a few days and rivers burst their banks.
Landslides have buried houses in Bosnia and reports say as many as 16 people may have died.
An outer suburb of the Serb capital Belgrade has been inundated and eight people are reported to have drowned.
Serbian PM Aleksandar Vucic told reporters the first bodies had been recovered in Obrenovac, the worst-hit area to the south-west of the capital, and he feared more would be found.
But he said the number of deaths would not be made public until the waters had receded.
A new flood surge was expected on the Sava River late on Sunday, he said.
In some areas, flood waters reached the second floor of people’s homes.
“The flash floods woke my uncle at around 0330 so they went up to the first floor. Then they had to go to the third floor because all lower floors were flooded,” one resident from Obrenovac said.
Rescue workers have been working to bring thousands of stranded residents to safety and officials have also ordered the evacuation of another town, Baric, closer to Belgrade.
The Sava River has risen particularly high in the western town of Sabac, and volunteers have tried to shore up flood defenses there.
Rescue co-ordinator Predrag Maric appealed for food, water, and clothing to help those in need.
One of the worst-hit areas in Bosnia is the eastern town of Bijeljina where rescue teams are trying to transport 10,000 people to safety.
Among those who drowned were 10 people in the Bosnian Serb Republic, police told local media. Six bodies were found in the northern town of Doboj and there are fears that more people have lost their lives.
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