There are estimates of five deaths to date in relation to political campaigning ahead of the Papua New Guinea election started on Saturday week.
The National newspaper reports a man was shot dead by police at a political rally in the Southern Highlands' Nipa district on Wednesday, while two others were reportedly shot at from a car carrying a candidate outside Kagua district station in the province on Tuesday.
The paper says the relatives of the dead men want the candidate, sitting MP, Aiya James Lagea, arrested.
They claim he has a cache of weapons.
Mr Lagea told the paper he wouldn't comment at this stage, saying it is the desire of the people in the electorate that polling not be disrupted.
The killings bring to five the number of deaths following two killings last week in Chimbu.