By Colin Packham

CANBERRA, Feb 22 (Reuters) - Australia will quickly deliverthe result of a planned independent inquiry into parliament'sworkplace culture, the government said on Monday, as pressuregrows after a newspaper published a third accusation of rape.

Two female employees of Prime Minister Scott Morrison'sLiberal party said last week they had been raped by the same manin 2019 and 2020.

Both have yet to make a formal police complaint, butBrittany Higgins, who has spoken publicly about her allegedrape, said last week that she would do so, though it is unclearif she has lodged one with police.

Finance Minister Simon Birmingham, who is leading aninternal inquiry into workplace culture, said he wanted aninvestigation that is to be set up next week to be impartial.

"I want complete independence," he told AustralianBroadcasting Corp radio. "I want people to have full confidencethat this enquiry is genuinely an independent (one)."

The complaint process is expected to be a central element ofthe investigation, he said, adding, "This is not something thatI expect to drag on for weeks."

Fuelling pressure on Morrison, the Australian newspaperpublished on Monday the account of a third woman, who said shehad also been raped by the unnamed former Liberal party workeron the night of June 29 and the morning of June 30 in 2016.

"I believe his actions constitute sexual assault, because heperformed or tried to perform sexual acts on me while I wasseverely intoxicated and unable to provide valid and informedconsent," the unidentified woman told the paper.

The incident happened outside parliament, she added.

Already dogged by accusations of improper behaviour towardswomen, Morrison's Liberals face a barrage of criticism about theway it handled Higgins' internal complaint to Linda Reynolds,who is now defence minister.

Higgins has said she felt pressure not to proceed with aformal complaint for fear of losing her job.

Reynolds last week apologised to Higgins but denied thatshe or her staff pressured her not to pursue a police complaint.

Morrison said he only learnt of the alleged complaints lastweek, and has sought to placate public anger with an inquiry.(Reporting by Colin Packham; Editing by Clarence Fernandez)