Mrs Bishop was in the running to lead the Inter-Parliamentary Union, an organisation of parliaments that promotes democracy.

She came second to Bangladesh's Saber Chowdhury in the second and final round of voting at the IPU's assembly in Geneva. There were also candidates from Indonesia and the Maldives – meaning Australia was competing against a trio of Muslim states.

Fairfax Media understands the controversial Parliament House burqa announcements, Prime Minister Tony Abbott's threat to "shirt-front" Russian President Vladimir Putin and even Australia's controversial new national security laws could have cost Mrs Bishop votes.

Mrs Bishop was criticised for her decision this month – made with Senate President Stephen Parry – to confine women wearing "facial" or "identity coverings" to glass-enclosed viewing galleries in Parliament House, separate from other visitors.

Mr Abbott asked Mrs Bishop and Senator Parry to reconsider the proposal after an extraordinary backlash. The matter remains unresolved.

A source close to the IPU told Fairfax Media they "couldn't believe that Bronwyn Bishop would associate herself with this idea of segregating women because of what they are wearing".

The source said IPU Muslim member nations would be offended by the ban.

An absolute majority was needed to secure the IPU presidency, with the 145 delegations holding two to five votes each. Australia had five: the Coalition's Nola Marino and Senator Cory Bernardi, Mrs Bishop herself and Labor's Tony Zappia and Senator Glenn Sterle.

It was reported on Thursday that the Labor members would not support Mrs Bishop but Senator Sterle told Fairfax Media this was not the case.

"It gave me heartburn but I did vote for her. I lost sleep over it but at the end of the day I'm an Aussie," Senator Sterle said. "I couldn't come over here and not vote for an Aussie."

Labor MPs Joel Fitzgibbon and Michael Danby, as well as former Labor Senate president John Hogg, were actively supporting Mrs Bishop's campaign.

With no candidate achieving the necessary majority in the first round of voting, the candidate from the Maldives was eliminated and the rest went on to a second round.

In the second round secret ballot, Mr Chowdhury received 169 votes, while Mrs Bishop and Indonesia's Nurhayati Ali Assegaf received 95 and 57 votes respectively.

Before the vote, a spokeswoman for the IPU told Fairfax Media that multiple voting rounds were the "likeliest scenario" due to the high number of candidates.

Congratulations to new President of IPU. Commiserations to Bronwyn Bishop who ran strong campaign to finish second. #IPU131 — Cory Bernardi (@corybernardi) October 16, 2014

Turn for #Australia's candidate. Bronwyn Bishop addresses #IPU131 Governing Council @IPUparliament pic.twitter.com/vNnL6q6c9x — IPUparliament (@IPUparliament) October 16, 2014

I don’t speak for IPU Asia Pacific region but for whole of IPU - new @IPUparliament president Saber Chowdhury #IPU131 — IPUparliament (@IPUparliament) October 16, 2014

I will not vote to whom fight Islam, even if she is a woman #IPU131 — سوسن تقوي (@SawsanTaqawi) October 16, 2014

I asked the #Australian Speaker of the house; Brownyn Bishop an unwelcomed question about the new draconian Aussie media laws at the #IPU131 — Birgitta Jónsdóttir (@birgittaj) October 12, 2014

The 53-year-old Mr Chowdhury will take over from Morocco's Abdelwahad Radi.

Mr Chowdhury is a veteran politician who was once imprisoned for his views and was recognised by Amnesty International as a "prisoner of conscience".

"Politics and public service is about helping people to solve their problems, to live their dreams," Mr Chowdhury said. "My belief is to always improve upon what you find and leave a better, more peaceful world."

He will serve a three-year term at the helm of the IPU.

A spokesman for Mrs Bishop declined to comment.

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