Torrential downpours at the weekend washed away vehicles and brought down buildings in the hillside town of Katesh, 300 kilometres (185 miles) north of the capital Dodoma.
"Two more bodies were found in the ongoing search and now the death toll has reached 65," said Prime Minister Kassim Majaliwa.
Images broadcast on television showed debris from houses, including furniture, strewn across streets, with key roads, power lines and communication networks disrupted.
"From around five in the morning (on Sunday), I heard loud bangs outside the house. When we tried to escape, it was too late because mud, trees and stones were rolling from the mountain," said a man named James, who had lost his wife and daughter in the disaster.
Some 5,600 people have been displaced by the landslides, said Mobhare Matinyi, a government spokesman.
Rashid Ntandu, 24, lost his house in the disaster and found shelter in a school in Katesh which has been turned into a refuge centre.
"I believe there are more bodies covered by mud," he said.
The disaster has prompted President Samia Suluhu Hassan to cut short her visit to Dubai for the COP28 climate talks, with her office saying she would visit the affected area on Thursday.
Tanzania and its East African neighbours Kenya, Somalia and Ethiopia are battling flash floods caused by torrential rains linked to the El Nino weather pattern.
The floods are exacerbating the humanitarian crisis in the region just as it emerges from the worst drought in four decades that left millions hungry.
Between October 1997 and January 1998, widespread flooding caused more than 6,000 deaths in five countries in the region.
Scientists say extreme weather events such as flooding, storms, droughts and wildfires are being made longer, more intense and more frequent by human-induced climate change.
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