"There is a lot of the Indigenous out there who want recognition and I think this a great way for white Australia to extend the olive branch," she told NITV News.
Her comments come in a week that has seen the debate about changing Australia's Constitution to positively acknowledge Aboriginal and Torres Strait Islander peoples put back on the agenda.
Advocacy group Recognise, which receives millions of dollars in government funding to raise awareness about the issue, released research earlier this week that showed overwhelming public support for recognition.
Of the 2,700 people surveyed, 75 per cent said they would vote 'yes' in a referendum to change Australia's Constitution. About two-thirds of those considered Conservative supporters said they would back the movement, along with nearly every Aboriginal and Torres Strait Islander person polled.
However, South Australian Liberal senator Cory Bernardi said movements like the Recognise campaign generally fail.
"Let me tell you that anything that seeks to divide our country by race, and every proposal that I've heard of seeks to do exactly that, I think is doomed to fail," he told the ABC's AM program on Thursday.
The whole campaign to remove racist clauses from Australia's constitution isn't a priority for the Government, Senator Bernardi said.
"What I would say to you, within the Coalition is that virtually no-one is talking about this."
"What I would say to you, within the Coalition is that virtually no-one is talking about this. Like most of Australia, this is a fifth-order issue at best."
Jacqui Lambie, who traces her heritage through Tasmanian tribal chief Mannalargenna, said the conservative Senator is out of touch.
"I don't give a stuff what Cory Bernardi says, he's wrong"
"If it's going to make the Indigenous feel included along with Australian white people, then why wouldn't we do it? Why wouldn't we change the Constitution to make that happen? I don't give a stuff what Cory Bernardi says, he's wrong," she said.
Almost since she was sworn into the Senate, Senator Lambie has pushed for dedicated seats for First Nations people in Australia's parliament. According to the Senator, dedicated seats would reduce the life expectancy gap between Indigenous and non-Indigenous Australians and improve their involvement in decisions affecting Aboriginal and Torres Strait Islander people.
"Let's extend the olive branch. It's not that difficult. The only people making this difficult are Tony Abbott and the Liberal Party. They're the only thing standing in the way. If they wanted something to happen, they'd make it happen."
The Attorney-General has told the media that the Abbott Government will be meeting with Indigenous leaders in Canberra in the next few weeks to revive the issue and decide on a way forward.
The Joint Parliamentary Committee on Constitutional Recogntion, led by Aboriginal politicians Ken Wyatt and Nova Peris, is due to release its final report on the issue before the end of June.