The state fire department on Tuesday confirmed 16 deaths in the city of Juiz de Fora and seven in Uba, about 110 km away.
President Luiz Inacio Lula da Silva offered his condolences in a post on X.
"Our focus is to ensure humanitarian assistance, the restoration of basic services, support for displaced people, and aid for reconstruction," he wrote.
About 440 people have been displaced in Juiz de Fora, the city hall said, as the rain triggered flooding and landslides and forced the suspension of classes in schools.
Specialised teams have mobilised to respond to incidents and search for missing people, it added. The state fire department said 136 officials - including 108 in Juiz de Fora and 28 in Uba - were deployed.
The department reported that 43 people were missing in Juiz de Fora, with another four people missing in Uba.
"It's a precarious situation; many people are missing. But by helping each other, we'll eventually find everyone," Gabriel Vitor, a 24-year-old state firefighter deployed to Juiz de Fora, said.
Brazil's government has recognised a state of calamity in Juiz de Fora, speeding up relief and humanitarian aid, it said in a statement.
Much of Brazil enters the peak of its rainy season during summer, from December to March, bringing frequent intense downpours, thunderstorms, flooding and mudslides.
"It was terrible; words can't describe how sad it is. Just ask God to find those who survived and to perform a miracle," said Jaqueline Teixeira, a 45-year-old Juiz de Fora resident.
The Juiz de Fora city hall said this has been the rainiest February in the city's history, with rainfall already more than double the amount expected for the month.
Mayor Margarida Salomao said in a statement on social media that the situation was "critical."
Brazil's National Institute of Meteorology issued on Tuesday heavy-rain alerts for parts of 14 states, including the entire area of Minas Gerais and Rio de Janeiro.
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