An inquiry into the abolition of the Aboriginal and Torres Strait Islander Commission (ATSIC) has found little support for maintaining the organisation, so far.

However, there is widespread concern over the mainstreaming of funding.

The Senate committee has agreed to make the 80 submissions it has received so far public.

It has also decided that further public hearings will be held in Darwin, Gove, Cairns and four other capital cities.

Committee chairwoman Senator Trish Crossin says while there is virtually no one defending ATSIC and its executive arm ATSIS, there is widespread concern over the transfer of the funding to government departments.

She says models may vary on how the money should be managed but there is a general feeling Indigenous people want a greater say.

"We don't want bureaucrats in main stream departments making those decisions for us," she said.

Senator Crossin says there is also resounding support for an nationally elected Indigenous lobby group.