Outspoken Palmer United Party senator Jacqui Lambie says she is willing to take a DNA test to prove her Indigenous heritage.

In her maiden speech to Federal Parliament, the Tasmanian claimed a family connection with a prominent Aboriginal leader from the state's north-east.

"We trace our history over six generations to celebrated Aboriginal chieftain of the Tasmania east coast, Mannalargenna," she told Parliament.

The claim drew scepticism from some in the Aboriginal community, with Tasmanian Aboriginal Land Council (TALC) chairman Clyde Mansell calling it "absolutely outrageous and scandalous".

However, Senator Lambie will not be deterred.

"I know what's in my blood," she told reporters in Hobart.

"If Mansell wants to take me on, I guess I'll meet him up at the hospital and both have a DNA test and see how we go once and for all."

Mr Mansell dismissed the challenge, saying DNA tests are not conclusive in proving Indigenous heritage.

"The matter of fact with Jacqui Lambie is her claim to be of Mannalargenna is not factual," he said.

Last week Senator Lambie said she was subjected to online threats of violence following her claim.

She intends to use the next sitting of Parliament to detail some of the threatening posts.

Lambie wants Indigenous quota in Parliament

Senator Lambie also said there should be up to five Indigenous MPs in the Lower House and four in the Senate, to reflect the percentage of Aboriginal or Torres Strait Islanders in the community.

She believes a new representative body proposed by Indigenous leader Noel Pearson would be prone to corruption and a waste of taxpayers' money.

"I just want to see Indigenous quotas," she said.

"They were the first people on the land in Australia and I think that out of respect to them, we should give them a quota.

"I've been consulting off and on it for years obviously with my Indigenous background so when you're around the Indigenous people you consult with them and you ask them what their concerns are.

"And to me they're saying we need voices in Parliament."

'Anyone supporting sharia law should leave Australia'

Meanwhile, Senator Lambie said anyone who supports imposing sharia law in Australia should be banned from receiving Government handouts and lose their right to vote.

Senator Lambie made the comments while discussing Australia's role in an international mission to combat Islamist extremists in Iraq.

She said Sharia, or Islamic law, is an underlying problem in Australia that needs to be addressed.

"I just say anyone who supports sharia law in Australia should not have the right to vote, should not get government handouts and should probably pack up their bags and get out of here - that's what I'm saying," she said.