"No arrests have been made yet but it's a promise that we are going to [make arrests] before sunset," said Lieutenant-Col Mzukisi Fatyela.
Fatyela said a 67-year-old woman sustained severe burns and died when the group set her flat alight in the first incident at 23:30 on Monday.
Her 16-year-old grandson was stabbed but survived the attack while a 6-year-old girl escaped unhurt.
A shack belonging to the woman's 26-year-old son was also set alight. He was not there at the time.
About 30 minutes later, the home of a 62-year-old woman was set alight.
She was stabbed and sustained burns and was in a critical condition in hospital, said Fatyela.
Meanwhile, her 35-year-old son was hacked to death and another son and daughter, aged 25 and 30, were in hospital. One had sustained stab wounds and the other burns.
Five grandchildren escaped unhurt. Their ages were not immediately known.
"Police are at the scene and we will check on the victims in hospital," said Fatyela. "We believe both cases are linked," he said.
Cases of murder, attempted murder and arson had been opened.