The move came just hours after the Parliament's presiding officers announced the security measures on Thursday, under which women wearing coverings would be forced to sit with schoolchildren in a glassed-off area of the public galleries.

Fairfax Media has learnt that, In an embarrassing back-down for the government, Mr Abbott will ask Ms Bishop and Senator Parry to reconsider the proposal after an extraordinary backlash.

Before the revised security rules were announced, Foreign Affairs Minister Julie Bishop and Attorney-General George Brandis both appeared to distance themselves from comments the Prime Minister made about the garment being confronting.

Ms Bishop agreed that people entering the Parliament should be identifiable but said that, unlike the Prime Minister, she did not find the garment confronting.

"I'm not confronted by clothing ... some may be offended by it, some may be confronted by it but in Australia we have a choice, and that's that kind of choice and society we fight to defend," she said.

The Prime Minister remains firmly committed to increasing security in private areas of Parliament House, including through the provision of photographic identification.

But the plan for the public galleries is effectively dead, with Mr Abbott having told colleagues that once someone had been screened he was more relaxed about facial coverings being worn.

Ms Bishop and Senator Parry announced the plan to segregate Muslim women on Thursday while police agencies undertook a review of security arrangements in Parliament House.

They said the step would require "persons with facial coverings entering the galleries of the House of Representatives and Senate [to] be seated in the enclosed galleries. This will ensure that persons with facial coverings can continue to enter the chamber galleries, without needing to be identifiable."

Senator Parry said the change was an interim measure and that "if there is an incident or someone is interjecting from the gallery, which as senators would know happens from time to time, they need to be identified quickly and easily so they can be removed for that interjection".

The announcement provoked a storm of protest from the opposition, the Greens, human rights and religious groups and prompted questions about Mr Abbott's call for Muslim leaders to support "Team Australia" and back his new counter-terrorism laws.

Liberal senator Cory Bernardi had asked for a ban on the garment to be considered. Liberal MP George Christensen and Palmer United senator Jacqui Lambie had also criticised the head covering.

The decision to segregate women with head coverings came after Fairfax Media revealed on Wednesday that Mr Abbott's chief of staff, Peta Credlin – who is one of the most influential people in the government - had privately told Mr Christensen she also supported a ban on the garment in Federal Parliament, for security reasons.

That prompted the Prime Minister to express sympathy on Wednesday for those of his MPs who had concerns about the burqa on security grounds and to argue Parliament should be governed by appropriate rules that require people to be identifiable.

He declined to comment publicly further on the matter on Thursday but, behind closed doors, senior Coalition MPs expressed dismay at the debate over the Muslim head covering.

When the new rules were announced, Muslim Women's Association executive officer Maha Abdo said the ruling created division and could rupture "Team Australia".

"I can't believe they are segregating us. Muslim women wearing the niqab [a veil similar to the burqa but which leaves the eyes uncovered] don't go into Parliament in high numbers," she said.

The NSW Bar Association issued a statement in response to the developments in Parliament on Thursday.

"Comments and actions which purport to link the wearing of clothing based on religious beliefs to risks relating to terrorism and particular races, nationalities or ethnicities may constitute racial vilification under the [NSW Anti-Discrimination Act] or offensive behaviour under 18C of the Racial Discrimination Act," said Arthur Moses, SC, the junior vice-president of the association.

Human Rights Commissioner Tim Wilson said there was "no justification" for the new security arrangements and that "if there was a danger, then why would we sit people with children?"

Opposition Leader Bill Shorten said he had sought an explanation of the ruling from Ms Bishop and he was "not sure why a person needs to be kept behind glass once they've been identified and security screened".

After Fairfax Media revealed the plan would be killed off, Mr Shorten said bluntly that people should not have to be segregated to attend Parliament.

"Leaders have a responsibility to act for minorities as well as majorities," he said.

"This divisive debate was allowed to drag on for too long because of the Prime Minister's silence. He is following his party instead of leading it."

Constitutional scholar George Williams said section 116 of the constitution covered religious freedom but "that only protects people against Commonwealth laws; it doesn't sound like there is Commonwealth law in this case, in which case the protections are not likely to apply, so yes, I think this can be imposed without a constitutional problem".