Making the announcement on Sunday in Darwin, Mr Abbott said it was important that the government continue as usual "despite the grave announcement we have made this morning".
"It is my intention to be in Arnhem Land for the week I promised," he told reporters.
Despite the remoteness of the indigenous communities he is visiting, the prime minister said he would be in regular contact with Canberra via secure communications provided by the Australian Defence Force.
The trip is the fulfilment of an election promise made to Yolngu elders in August last year.
Mr Abbott will participate in conservation work with rangers on a remote island, meet with school attendance officers, visit a cattle station and a local war memorial, and view a NORFORCE operation.
He is due to return to Canberra on Friday evening.
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