About 16,000 people had already returned to their homes, the ministry said in a statement, as water had receded in some regions. But evacuations continued in North Kazakhstan, Aktobe, West Kazakhstan regions, it said.
The figures come a day after Kazakhstan's president described floods across the north of the country as a national disaster and ordered his government to free up funds for relief efforts by cutting spending elsewhere.
In Russia, also hit by the worse floods in living memory, a top ally of President Vladimir Putin said regional authorities had fallen short in their forecasting and emergency response.
Water levels in rivers in swathes of Russia's Ural and southwestern Siberian regions, as well as adjacent areas of Kazakhstan, were still rising rapidly, officials said.
The disaster has been caused by the fast melting of large snowfalls amid heavy rain, swelling the tributaries of several of Europe's largest rivers.
Kazakh President Kassym-Jomart Tokayev arrived in Petropavlovsk, where the local governor said 10,345 people had been evacuated as parts of the city remained under water.
"We are going through tough times. This is a disaster of a national scale," Tokayev told residents. "I think the next 10 days will be critical, but we are already taking measures to rebuild the country and deal with the aftermath of this disaster."
Tokayev’s office said that in order to free up money for disaster relief, he had ordered the cabinet to cut all non-essential budget spending and cancel some events, including an economics and international affairs conference in the capital.
The Caspian Pipeline Consortium (CPC), which handles some 1% of global oil, said it was working to protect its facilities from floods in Kazakhstan's Atyrau region.
In Russia, Security Council secretary Nikolai Patrushev said "huge material damage could have been minimised" if regional authorities had paid more attention to forecasting the water levels and responding more effectively.
Some people in the affected areas have also expressed frustration with the authorities.
"I don't want to blame anyone, but if it was known from mid-March that the flood would be severe, why didn't the city and regional administration do anything?" one resident of the Russian city of Orenburg posted on social media.
Others mocked the authorities for carrying out non-urgent renovations on a street in the centre of the city instead of focusing on dams. "Orenburg is drowning, and they are removing tiles," one person wrote.
In Kurgan, some locals singled out regional governor Vadim Shumkov for criticism. "Why is there such a mess going on here?" one resident posted.
But another Kurgan local, who gave his name as Oleg, told Reuters the authorities had done "good work" ahead of the floods to strengthen the dam and evacuate residents.
"I haven't seen such protective measures in my whole time in the city," the 47-year-old said, adding that the floods had not yet reached his neighbourhood and he was staying put for now in his multi-story apartment building.
