The appointment would be Australia's first to the powerful body, coming amid criticism of its own human rights record against indigenous people and asylum seekers in offshore detention centres on Nauru and Papua New Guinea's Manus Island.
"We didn't use our aid budget, we didn't make promises we couldn't keep," the paper quoted Bishop as saying on Friday in the Serbian capital of Belgrade. "We very much campaigned on our record and how we would act on the Human Rights Council."
Australia secured 141 written pledges and more than 20
verbal pledges from 192 U.N. members to back its bid, the paper said.
On Saturday, Bishop's office said it could not confirm Australia had been guaranteed a spot, but added, "We are looking forward to making a positive contribution," ahead of October's announcement of the council's composition.
The U.N. has previously criticised Australia's treatment of its indigenous peoples, with a report from its special rapporteur, Victoria Tauli-Corpuz, due in September.
The report, on her 15-day visit in March, reviewed the impact of laws surrounding the government's 2007 intervention aimed at curbing alcohol abuse, domestic violence and improving the health of indigenous Australians in remote communities.
France's foreign ministry announced its withdrawal in a statement on Thursday that backed Spain's bid for the second vacancy.
(Reporting by Benjamin Cooper; Editing by Clarence Fernandez)
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