Deep divisions over the future of Islam in Australia have emerged after calls for the adoption of sharia law in submissions to a federal parliamentary inquiry into multiculturalism.

Citing existing Government support for Islamic banking and laws governing halal meat - and backing from the Archbishop of Canterbury - Muslim organisations have urged recognition of the religious law to boost integration.

But Attorney-General Robert McClelland has rejected the move, repeating the stand taken earlier by both John Howard's former Coalition Administration and the present Labor Government.

The call has also drawn heavy fire from Jewish and Christian groups, and right-wing opponents of present immigration and multicultural policies.

"[We] plan to take every lawful action and use every lawful means to inhibit Islam in Australia," the far-right Australian Defence League said in its submission to the joint standing committee on migration.

Some Islamic groups already regard the debate as more about Muslim integration and assimilation than multiculturalism.

"The overwhelming majority of Australian Muslims want nothing more than to get on with their lives and make meaningful contributions to this wonderful country," the Islamic Council of Victoria said.

"Constantly being singled out and problematised makes this so much harder to do."

Sharia law is already used to give religious force to divorces formalised by the Family Court and to settle business and other disputes within Muslim communities, but does not have the force of law.

The Australian Federation of Islamic Councils wants that to change.

Federation president lkebal Adam Patel said Islamic law was part of a Muslim's culture and denying any recognition of this went "directly against any profession of multiculturalism".

Calling for official recognition of sharia, Patel said when Muslims advocated creating arbitration systems similar to those existing in some countries for Jewish and Christian communities, they were labelled radical and extremists.

Canada's Ontario province had rejected sharia while allowing Jewish and Catholic arbitration, as had Britain's former Labour Government.

But Patel said the Archbishop of Canterbury had regarded the adoption of some aspects of sharia in Britain as unavoidable, and had said this would help maintain social cohesion.

Patel's submission said that in Australia, the federal Government had promoted the development of Islamic finance as an alternative source of wholesale funding.

The Government had said it would use tax breaks and other measures to attract Islamic banks to Australia, lure investment in Australian assets from sharia investors, and allow the establishment of sharia-compliant investment products.

The federal Government also had legislated sharia requirements, with Halal red meat production for export governed by the Australian Government Muslim Slaughter Programme, which allowed only approved Islamic organisations to certify Halal products.

"Muslims in Australia should accept Australian values, and Australia should also provide a 'public sphere' for Muslims to practise their belief," Patel's submission said. "It takes two to tango."

But the Australia/Israel and Jewish Affairs Council said Muslim communities faced the prospect of social exclusion, with such organisations as Hezb ut-Tahrir, encouraging isolation to prevent adherents from being "tainted" by Australian society.

Stefan Slucki, the convener of the Presbyterian church and nation committee, said members who had fled Islamic persecution in the Middle East needed reassurance that sharia law would never become a parallel legal system in Australia.

"Some aspects of sharia can appear benign but in [others] its thrust is harmful to the social consensus of the Judeo-Christian framework of a Western country," his submission said.