Nearly one thousand people took to the streets on Saturday to protest alleged police brutality against campaigners calling for the independence of the so-called eastern Lunda Chokwe region.
Police fired on protesters as they headed from Luzamba to Cuango, an administrative town about 600 kilometres east of capital Luanda, activists said.
Cuango is in the north of the vast region that separatists want to see independent and comprises Angola's entire eastern half, according to some claims.
Another demonstrator was shot in the head and hospitalised, he said, adding that the protesters were unarmed.
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"There are actually only 51 detained out of a total of 78 arrests. Thirteen people were injured, including four women and a 17-year-old. The others have been freed. In Cuango there was one death," a senior police officer told AFP.
Clashes were also reported in Saurimo, in the northeast of the Lunda-Norte province, some 400 kilometres east of Cuango.
"The regime must stop shooting at people who march peacefully and are only exercising their rights," he said.
Angolan authorities arrested five Lunda Chokwe activists in March 2016 on suspicion of attempting to murder a police officer. They remain in prison.
Dos Santos's government has been criticised as secretive and corrupt, with authorities crushing dissent.
Dos Santos, 74, who has been in power since 1979, is accused of having used the State to direct money to his relatives by putting them in charge of major public enterprises. Meanwhile Angola's citizens suffer dire poverty.
The Front for the Liberation of the Enclave of Cabinda (FLEC) has been fighting for the independence of Cabinda, an oil-rich Angolan enclave located inside Republic of Congo, for four decades.
The province produces 60 per cent of Angola's oil, making the country, along with Nigeria, one of sub-Saharan Africa's largest oil producers.