Prime Minister Tony Abbott is calling for the Speaker to back down on plans to ban women who cover their faces from sitting in Parliament's main public galleries.
The Speaker and the Senate President will still make the final decision about security arrangements in Parliament House.
But the ABC understands Mr Abbott will tell Bronwyn Bishop that "common sense should prevail" when it comes to public access to Parliament House, including the galleries of the House of Representatives and the Senate.
It is believed Mr Abbott will argue that if people have been appropriately screened on the way into the building, including perhaps being asked to show their face, then they should be allowed to cover their faces and go about the public areas like anyone else.
He regards it is as a "people's house" and believes it should be treated as such.
But Mr Abbott "does not resile" from the fact that the secure or private areas of Parliament House like the ministerial wing require a heightened level of security.
It is understood he would prefer that the identity of visitors to the private areas be checked at the screening point by their faces being uncovered, and then "constantly verified" as they walk around.
This appears to be a step up from the current requirements for someone to temporarily remove their facial coverings at a security screening point.
Two ministers have told the ABC the decision to segregate people with face coverings was a mistake, with one describing it as "incredibly foolish".
A number of backbenchers have backed the sentiment.
The Department of Parliamentary Services (DPS) announced on Thursday: "Persons with facial coverings entering the galleries of the House of Representatives and Senate will 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."
The enclosed galleries are usually used by visiting school parties.
Race Discrimination Commissioner Tim Soutphommasane said Mr Abbott's intervention was a welcome development.
"I saw no good reason to be putting Muslim women in burkas or niqabs in a designated glassed area," he said.
"People were genuinely worried that this was going to set a dangerous precedent.
"Once you set off a particular part of public space and say that is where people of a certain background should sit, it can only be a matter of time before others start suggesting that perhaps we should consider parts of our buses or trains, our cafes or restaurants to be set aside for people with a certain background as well.
"That would be a dangerous development."
Shorten accuses PM of following party, 'not leading it'
Opposition Leader Bill Shorten said leaders had a responsibility to act for minorities as well as majorities.
"If we're asking our troops to stand up to sectarianism, intolerance and prejudice overseas, we should be prepared to do the same in our Parliament," he said in a statement.
"People shouldn't be segregated to attend Parliament.
"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."
Human Rights Commissioner Tim Wilson said the decision to force people to watch from behind a glass screen sent the wrong message.
"Clearly setting up a system where depending on how you manifest your faith you may be facing one type of treatment to another type of treatment ... seems utterly unjustified," he said.
"The Prime Minister himself yesterday (Wednesday) talked about the fact that no-one's even in Parliament House, as far as he's aware, wearing a burka, let alone sitting in the public gallery."
Independent MP Andrew Wilkie likened the rule to "religious apartheid" and said it was "deeply wrong".
Muslim Women's Association chief executive Maha Abdo said a ban on burkas would make some women afraid to leave their homes.
"We are pushing them back into their homes, we're pushing them away from society that we want them to be part of," she said.
She said attacks against women wearing Islamic clothing in Australia were increasing and that the decisions of Muslim women around their dress should be respected.
"If it is, what they're saying, a security threat, explain to us what it is and I'm sure we can work together on that," she said.
Recently senator Cory Bernardi called for burkas to be removed at security checkpoints at Parliament House and senator Jacqui Lambie called for burkas to be banned in public.
On Wednesday, Mr Abbott said he wished the garments "were not worn" in Australia, but indicated he would not support a general ban because Australia was a "free country".