Game rangers have killed three poachers in the past week during an escalation of armed incursions into South Africa's flagship wildlife reserve, where hundreds of rhinos have been killed for their horns this year.

Paul Daphne, a spokesman for South Africa's national parks service, said poaching activity in Kruger National Park has traditionally increased in November and December before tapering off around the year-end period.

Some rangers refer to this phenomenon as "Christmas shopping" by poachers.

The parks service says a total of three poachers were killed in a shootout on Monday and two separate firefights on Thursday.

Three poachers were wounded and arrested in another confrontation on Wednesday.

Many poachers cross into the Kruger park from neighbouring Mozambique.