Bosnia, where a million people were without drinking water, was in official mourning, while Serbia, where 1.6 million have been affected, was due to follow suit on Wednesday.
Serbia's Prime Minister Aleksandar Vucics sounded the alarm over the possibility of disease as rising temperatures turn thousands of animal carcasses in the flood waters putrid.
"There are tons of dead animals that we must dispose of," Vucics said in parliament.
Health experts and army teams in Serbia and Bosnia wearing olive green protective uniforms were already working to decontaminate and disinfect the vast tracts of farmland under water.
Tons of dead animals have already been recovered, but muddy areas and landslides have hampered the effort.
The World Health Organisation said on Tuesday that it had sent an expert to advise Serbian authorities on sanitation and ensuring safe drinking water.
The WHO said it was also working to mobilise medical supplies, including supplies to fight diseases commonly spread by floods, such as illnesses that cause diarrhoea.
"We will face a major fight against epidemics and infectious diseases, which are inevitable after such floods," said Nermin Niksic, Muslim Croat Federation prime minister, one of the two entities that make up post-war Bosnia.
EU countries step up aid
An intense deluge of rain last week caused the fast-flowing river Sava and its tributaries to burst their banks, leaving huge areas under water and causing hundreds of landslides.
More than 100 000 people have been evacuated in Bosnia in the worst exodus since its 1992-95 war, while in Serbia some 30 000 have had to flee their homes.
In Croatia, some 15 000 people have been evacuated, including 4 000 in Gunja, where waters flooded the whole village. Two people have been killed, and one person remains missing.
Officials in Bosnia also warned on Monday that some 120 000 unexploded mines left over from the Balkan wars of the 1990s could be dislodged and moved.
In Obrenovac, the Serbian town worst affected with more than half of the 20 000-strong population evacuated, health authorities on Tuesday began the gruesome task of removing victims.
On Monday, Vucics said 14 bodies had been found in Obrenovac so far. Half of them drowned, the others died of natural causes. The toll could still rise.
Authorities in the Balkans have also begun assessing the damage, which is expected to reach hundreds of millions of euros.
Vucics on Monday said some analysts have estimated the cost to "rebuild a lot of roads, bridges and renew the infrastructure, which will not be easy", could reach up to $1.4bn.
"We are expecting significant help from foreign governments, we need a lot of medicine, food, and especially baby food and construction material," he said.
The European Commission said on Tuesday that 19 EU states had now offered assistance, with close to 400 relief workers from member countries on the ground.
Kristalina Georgieva, EU commissioner for humanitarian aid and crisis response, met in Belgrade with government officials.
"Now, immediately, we will make funding available to meet the immediate humanitarian needs of the affected population," Georgieva said.
Equipment and humanitarian items would also be shipped from member states to Serbia.
Nato Secretary General Anders Fogh Rasmussen was due in Sarajevo on Wednesday.
Belgrade braces for floods
In parts of Bosnia, water levels have begun to fall but in Serbia they were still rising on Tuesday and were expected to reach a peak later this week.
In the Serbian capital Belgrade, where the Sava flows into the Danube, volunteers have been working around the clock to make a wall of sandbags 12km long to protect the city.
"I didn't hesitate at all," said Milenko Pajic, an 18-year-old student helping with the flood defences. "If my grandfather could fight for his country with arms, I can pack up and pile up sandbags."
Hydrologist Sinisa Mihajlovic predicted the Danube would swell further in the coming days but that it should "remain within the flood-defence limit".
Belgrade mayor Sinisa Mali said he was confident the capital was "ready" to face the rising waters.
"We are following the situation closely, and we are ready to intervene if needed," Mali told reporters.