Under threat of an electoral backlash from the Muslim community, Mr Palmer has been trying to hose down Senator Lambie's comments.

He told Fairfax Media on Wednesday he wasn't aware of Ms Lambie's comments but a string of text messages to Muslim community leader Keysar Trad indicate he is not only aware of her strident stance against sharia but has assured Mr Trad it is not PUP policy.

Ms Lambie said: "Anyone who supports sharia law in Australia should not have the right to vote, should not be given government handouts and should probably pack up their bags and get out of here."

Angered by her comments, Mr Trad, spokesman for the Islamic Friendship Association of Australia, said he contacted Mr Palmer and told him the Muslim community – much of which lives in key marginal seats – had been impressed with PUP's stance on the budget. But with three state elections on the horizon, he warned Mr Palmer against "alienating Muslim voters".

In response, Mr Trad said Mr Palmer told him: "We need to calm things down, give it a couple of weeks. I'm confident that others will be pointing out matters [to Senator Lambie]".

Mr Trad has offered to give Senator Lambie, PUP senators, and Mr Palmer a "cultural briefing" on sharia.

"A lot of people talk about sharia but what they have in mind is a tiny aspect of sharia," he said. "The penal provisions make up less than 1 per cent of sharia. Sharia is all the teachings of Islam and it is about being good to your neighbour, being honest, decent, not stealing, praying five times a day."

Mr Palmer told Fairfax Media before hanging up: "I don't know what those comments were. You should speak to Jacqui Lambie."

He did not respond to a further text message outlining the texts received by Mr Trad.

There has been persistent speculation in Canberra that Senator Lambie is not happy inside the PUP tent and may break from the party. She recently conceded there had been some "argy bargy" with Mr Palmer.

Labor senator Sam Dastyari took aim at Ms Lambie, saying her comments were "uninformed and irresponsible" and designed to connect the current fear about Islamic State fighters with ordinary peace-loving Muslims.

"Just because you can string the words Muslim, sharia and ISIS into a sentence doesn't make it right and doesn't make it factual," he said.

Parliamentary Secretary to the Minister for Social Services, senator Concetta Fierravanti-Wells, who is currently consulting with ethnic communities, also dismissed fears over sharia. 

"Sharia law doesn't operate in Australia and it is not going to operate in Australia," she said.