The statements have followed a ban on full face coverings that has just come into effect in France.
The federal Opposition's spokeswoman on the Status of Women, Michaelia Cash, has called the wearing of the burqa "un-Australian".
And she has added her voice to concerns that some Muslim women in Australia are being forced to wear it.
"There may well be some sectors of society where women are not equal and where they are potentially being ostracised. I think that this debate is very important so that women in Muslim communities, if they are being forced to cover their faces and it's not their choice to do so, actually understand that they are living in a country where freedom of choice is actually something we value."
Senator Cash has stopped short of calling on Australia to follow France by banning full-face coverings.
But she says she believes Australians place high importance on face-to-face communications, and any woman who covers her face won't be able to fully participate in Australian society.
"It's my personal opinion that not only the burqa but any apparel that covers a person's face is alien to our culture and our values as Australians. This kind of covering prohibits open communication, and being able to see someone's face in Australian society is crucial to how we operate."
Women's Interests Minister opposed
Western Australia's Minister for Women's Interests Robyn McSweeney is also opposed to full face veils.
She has urged Muslim women to refuse to wear the garments because, as she sees it, they are a symbol of female repression and "alien" to Australian culture.
Shameema Kolia is a Muslim woman who owns a health food store in Perth.
She chooses not to wear a burqa, but says Ms McSweeney's remarks stem from ignorance, and have done harm to the Muslim community.
"It's just creating this divide of us and them. And there is no 'us and them' because if you ask a Muslim person - if you ask me - I'm Australian, I'm Muslim and the two identities are not conflicted. We talk about multiculturalism. We talk about celebrating it. And here is a Minister who stands up and says that actually we are allowed to discriminate when it suits us, and that is unacceptable."
Western Australia's Multicultural Services Centre rejects the remarks against the burqa by the state Minister for Women's Interests.
Director Ramdas Sankaran says there are plenty of examples around the world of empowered women wearing the garment.
"What did we see happening in the Middle East in recent weeks and in parts of Africa, where women in burqa, amongst others, were in the front lines of the barricades standing up to the Gaddafis of the world? I mean is that a sign of oppression? Women in burqas have made notable contributions in many spheres of life across the globe. Now is that social isolation? Is that women not being able to achieve what they are? I think the Minister's gone overboard", he says.
Support from Muslim community
Yet there is some support in the Muslim community in Australia for restrictions on the wearing of face-coverings.
Doctor Ameer Ali is the Vice President of the Regional Islamic Council of South East Asia.
He calls the burqa and niqab "un-Islamic".
Doctor Ali says the coverings do not fit with modern values, and should not be worn in public places.
"All that the Koran wants from the women is to dress modestly. For men and women. So if you think covering from head to toe in a black garment then I think there is something wrong with the thought process", he says.
"The burqa and the niqab, these two are the most extreme forms of covering a women. It has no place in the holy book, the Koran. It is the living relic of patriarchal, medieval, misogynist society. That civilisation has gone.
Liberal Senator for South Australi Colin Bernardi has gone further than his party's official spokeswoman on women's affairs on the burqa issue.
He says Australia should follow France in banning the burqa, saying it isolates the wearer and poses a threat to security.
