Three men who attempted to enter Australia's Parliament House on Monday wearing a Ku Klux Klan hood, a niqab and a motorcycle helmet said they were unfairly treated under new regulations targeting Muslim face veils.

The men want Muslim veils that cover the face banned from the nation's seat of government and said their stunt exposed inequality in the security system that allows visitors to be so dressed.

The three Sydney residents – Sergio Redegalli, 52, Nick Folkes, 45, and Victor Waterson, 49 – were eventually allowed inside the building, but not with their headwear.

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"They have one rule for Muslim women and another for everybody else, and it's utterly sexist," Redegalli said.

The protest posed the latest quandary for Parliament House officials in their evolving security policy for dealing with Muslim face veils.

The department that runs Parliament House had announced earlier this month that "persons with facial coverings" would no longer be allowed in the building's open public galleries. Instead, they were to be directed to galleries usually reserved for noisy schoolchildren, where they could sit behind soundproof glass.

The policy was branded a "burka ban" and had been widely condemned as a segregation of Muslim women, as well as a potential breach of anti-discrimination laws.

Officials relented last week, saying people wearing face coverings would be allowed in all public areas of Parliament House.

According to the new policy, face coverings must be removed temporarily at the building's front door so that staff can check the visitor's identity.

When the trio arrived at the front door on Monday, a security guard told Redegalli that he could not enter wearing his KKK hood, and advised Waterson that he could not wear his full-face motorcycle helmet. Folkes initially was told he could enter wearing his niqab, but was later advised that he could not wear it inside.

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When Redegalli removed his hood, it revealed a niqab underneath, but the guard said he could not enter wearing it.

Television stations aired video of the exchange.

The Department of Parliamentary Services said in a statement that "protest paraphernalia" was not permitted inside Parliament House. It also said there has been a longstanding ban on helmets for security reasons.

Redegalli, an artist who created a stir in Sydney with a "say no to burqas" mural outside his studio a few years ago, said he was told by officials that men could not wear niqabs. He said he was told that the KKK hood could not be worn because it was a cultural rather than religious garment.

Security has increased at Parliament House since the government raised its terror warning level last month in response to the domestic threat posed by supporters of the Islamic State group.