Indigenous Affairs Minister Senator Amanda Vanstone has rejected the findings of a Senate report that wants a new nationally-elected Indigenous body set up to replace the Aboriginal and Torres Strait Islander Commission (ATSIC).

The committee's findings are a response to the Government's plans to abolish ATSIC and transfer its programs to mainstream departments.

Members of the committee from Labor and the minor parties want a new nationally-elected Aboriginal group with ongoing funding, which would be recognised as a primary source of advice on Indigenous views.

But Senator Vanstone says the Federal Government is not interested in that.

"We don't mind if Indigenous people want to get together and create what is an Indigenous construct, but we're not interested in developing one," she said.

"I mean that was the problem with ATSIC - it was a non-Indigenous construct put there so white Australians can say to themselves, 'oh, we are listening to Indigenous people' - I think it was lazy and inept."

Labor Senator Claire Moore says the committee wants the Federal Government to defer plans to scrap ATSIC regional councils until there is further consultation.

"No longer can Indigenous people in our country feel that when we are talking about the administration of Indigenous affairs that they are silent and invisible," she said.

Meanwhile, Liberal Senator David Johnstone says Labor is being hypocritical by criticising the Government's plans while supporting the abolition of ATSIC.

"What is the Labor Party proposing in terms of representation for Aboriginal people to replace ATSIC?" he said.

He also says the committee did not consult widely enough.