In a post on her Facebook page that has attracted more than 11,000 comments in 24 hours, the independent senator asked her followers to "vote yes or no" to whether Australia should be accommodating people fleeing the crisis torn region.

And in a Radio National interview on Wednesday morning, Senator Lambie appeared to suggest that refugees settled in Australia should be forced to wear electronic monitoring bracelets.

She also said Western forces should be establishing "safe zones" in Syria to prevent people from fleeing the country at all.

It comes as the first arrivals from Syria – a family of five from the devastated city of Homs – described Australians as "very fair and very kind" after they arrived in Perth on Monday night.

In a written statement, the father thanked "the Australian government for opening their doors and providing a better future for me and my children" and "everybody for giving us a chance at happiness".

He said his hopes for his family were to "educate my kids well, to find safety, to get a job, and live in peace."

Speaking from Manila, Prime Minister Malcolm Turnbull said, at this time, Australia had no plans to increase the one-off intake of 12,000 Syrian refugees.

Australia had a "long proud history" of taking in refugees, he said, but "it is important we take no more refugees than we are able to satisfactorily settle and settle well".

And he stressed that all immigrants to Australia underwent thorough security checks.

People responding to Senator Lambie's post were divided, with some sharing her sentiments that Australia should take an even tougher stance on refugees than it already has.

"One of those responsible for the Paris massacre was a supposed refugee. How do we know what we are letting into our country?" wrote one commenter, although the links between the Paris attacks and refugees remain unclear, with Germany's interior minister suggesting overnight that the refugee passport found in Paris may have been planted.

Another respondent to Senator Lambie's post lashed her for "starting a thread that spreads division and hate" and another warned her not to "become Pauline" with views akin to those held by Pauline Hanson.

Senator Lambie told Radio National on Wednesday: "We haven't tackled this very well. Why don't we have safe zones in Syria?"

"They talk about putting peacekeepers in, OK, why are these refugees fleeing? The worst thing we can do is let the refugees flee from their country," she said.

She said that incoming refugees should also be asked whether or not they support Sharia law.

When broadcaster Fran Kelly suggested that was not a rigorous method of screening, Lambie replied: "I think that question certainly needs to be asked, there's no doubt about that."

"No one's talked about putting security, electronic bracelets on them or anything like that, nobody's gone that far," she said.

"I think it's about time we put our foot down here.

"So maybe the first person who should have an electronic device put on them is the bloody Grand Mufti."

Senator Lambie's comments follow a number of calls this week for humanitarian arrivals from the Middle East to be barred.

NSW Nationals state MP Andrew Fraser called for Prime Minister Malcolm Turnbull to "close our borders" and Queensland Nationals MP George Christensen told News Corp the decision to accept 12,000 people should be revisited.

The government said this week that the 12,000 refugees would be "hand-picked" and subject to security strict security screening.

Immigration Minister Peter Dutton on Monday said the influx of refugees to Australia was entirely different to the situation confronting Europe.

Social Services Minister Christian Porter on Tuesday called on Australians to give the first arriving refugees "time and space to adjust to their new circumstances".

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