He arrived in Arnhem Land on Sunday, honouring an election promise to spend a week every year in an indigenous area.
Mr Abbott says he wants to hear from local people about community needs.
His visit comes a day after he committed Australian troops to the fight against Islamic State militants.
On Sunday Mr Abbott announced the deployment of 600 troops to the United Arab Emirates ahead of possible combat operations against Islamist militants in Iraq.
Late last week, Australia also raised its terrorism threat level to "high" for the first time in over a decade, amid concerns over the effect of Islamist conflicts on domestic security.
Mr Abbott said he would be in regular contact with Canberra. "Obviously, if there are dramatic new developments I can move if needs be," he said.
Referendum timetable
The prime minister, who is staying in a tent at a site sacred to the local community near Nhulunbuy on the north-east tip of the Northern Territory, was given a traditional welcome when he arrived on Sunday.
On Monday morning, he visited an indigenously-run sawmill and the site of a possible new bauxite mine.
Mr Abbott has described the visit as a chance to "gain a better understanding of the needs of people living and working in those areas".
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Phil Mercer, BBC News, Sydney
Painted Yolngu dancers greeted Tony Abbott on his arrival at Yirrkala in Arnhem Land, one of the largest Aboriginal reserves in Australia. He is camping near the mining town of Nhulunbuy where, according to legend, the didgeridoo was created by the revered spiritual figure Ganbulabula.
On a typically warm Northern Territory morning, Mr Abbott started the week at a site where an indigenous community hopes to develop a bauxite mine. Economic independence is the ambition of tribal leaders, and employment has been the focus of the conservative prime minister's first full day in the Top End of Australia.
In a rugged part of the country, there is a strong sense of goodwill towards Mr Abbott, who is seeing for himself the privations and cultural pleasures of life in such a remote corner of the Australian continent. Politicians from Canberra have made bold, but ultimately misguided, pledges about Aboriginal jobs and health in the past. Tony Abbott will not want to make promises he can't keep.
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Local indigenous leaders say they are seeking a renewed focus on a referendum for constitutional recognition of indigenous Australians.
Last year, parliament passed a bill recognising Aboriginal and Torres Strait Islander peoples as the country's first inhabitants, but the constitution contains no mention of them.
"I think we're all in favour of doing the right thing by Aboriginal people," Mr Abbott said.