The floods, considered the worst to hit the mainly Kurdish region since 1937, are expected to get worse as more rains are predicted in the coming days.
The floodwaters hit Batman on Wednesday evening, officials said, when rivers swollen by torrential rains swamped streets and toppled buildings, killing 11 people and triggering a major rescue operation.
Governor Haluk Imga said the damage to the province of Batman was more than $8 million.
"We will continue to give food as long as we can. We won't let down any of our citizens," he told a news conference. Government aid agencies have already provided food for 6,000 people in Batman.
Troops joined rescue services in helping to evacuate homes. Local authorities opened municipal buildings such as sports centres to house families fleeing the disaster.
At least seven people were treated for injuries in hospital.
'Neglect, not fate'
Diyarbakir, the biggest city in the region, was hit by floods on Tuesday night, the water rising with dramatic speed and taking thousands of residents by surprise.
"I suddenly found myself surrounded by water while sitting at home. My children and I climbed onto the roof to save ourselves"
Emine Gungoren, a housewife
"I suddenly found myself surrounded by water while sitting at home. My children and I climbed onto the roof to save ourselves," said housewife Emine Gungoren.
"We saw an artificial lake appear in just 15 minutes. Suddenly water and mud filled our homes," said Hasan Atmaca, a shop owner in Diyarbakir's Cinar district.
People were being evacuated from their homes by boat or trying to clear up the mess as the waters receded. Two people were still missing in the city.
A group of people protested at government offices in Cinar district, throwing stones and breaking windows.
The newspaper Milliyet attributed the high death toll in the impoverished southeast to poor construction and ageing infrastructure.
"Neglect, not fate," its headline read above a picture of flooded streets.
Roads linking Batman to Diyarbakir and other towns were closed to traffic.
Istanbul, Turkey's largest city, some 1,300 km northwest of Diyarbakir, and the Mediterranean cities of Antalya and Mersin have also suffered flooding in recent days.