As rescuers scrambled to find survivors from the Saturday quake, premier Kassim Majaliwa headed to the worst-hit city, Bukoba, to attend a mourning ceremony at its stadium.
President John Magufuli, who is from the region, said he was "deeply saddened."
Salum Kijuu, governor of Kagera province where Bukoba is located, told AFP "the current toll is 16 dead, 253 injured, 840 buildings destroyed, including 44 public buildings."
He said most of the casualties and damage occurred in Bukoba district itself. A group of 15 boarders at a boys' secondary school was believed to be among the casualties there.
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The quake struck at 1227 GMT in a region near Lake Victoria and the borders of Uganda and Rwanda, according to the US Geological Survey (USGS).
Its epicentre was 23 kilometres east of the northwestern town of Nsunga, in Bukoba district.
Bukoba suffered widespread damage, with 270 houses destroyed and electricity disrupted, the Red Cross said in a statement.
Its main hospital was stretched to nearly full capacity and had limited stocks of medicine.
"Telecommunications have been disrupted and we are trying to get a clear picture of the damage to hospitals and other essential infrastructure," Andreas Sandin, Red Cross operations coordinator in East Africa and the Indian Ocean Islands, said in a statement.
"Even the old people say they've never seen an earthquake as big as this in these parts," he added.
Earthquakes are fairly common in the Great Lakes region but are almost always of low intensity.
An AFP correspondent who has relatives in Bukoba said 10 family houses had collapsed.
No damage was reported in Tanzania's economic capital, Dar es Salaam, which is located some 1,400 km southeast of Bukoba.
"It's safe in Dar but we are still worried about the safety of our family," the AFP correspondent added. "The regional hospital is overwhelmed and can't handle any more patients.
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