The backdown followed a decision on October 2 by House Speaker Bronwyn Bishop and Senate President Stephen Parry to have a different seating for women wearing Burqa after a request from Liberal Senator Cory Bernardi to ban the religious headwear from being worn in the building.
Bernadi considered burqa as a symbol of oppression and un-Australian and wanted it to be banned from parliament on security grounds.
The government department that runs Parliament House announced earlier this month that "persons with facial coverings" would no longer be allowed in the open public galleries of the House of Representatives or the Senate.
However, hours before Parliament was to resume, the Department of Parliamentary Services said in a statement that people wearing face coverings would again be allowed in all public areas of Parliament House.
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But the face coverings would have to be removed temporarily at the security check point at the front door so that staff could "identify any person who may have been banned from entering Parliament House or who may be known, or discovered, to be a security risk," Sydney Morning Herald reported.
Abbott later said that he had not been notified in advance that the ban was planned and had asked Bishop to "rethink that decision."
"I asked the Speaker to re-think that decision and my understanding is that it was an interim decision, that it would be looked at again in the light of security advice that will come in coming days," Abbott had said.