Australia's razor-close election could end up in court, with the re-elected government holding out hope of extending its single-seat majority.

The candidate whom Prime Minister Malcolm Turnbull's conservative government hoped would deliver it a 77th seat in the 150-seat House of Representatives, Ewen Jones, conceded defeat Monday, a month after the July 2 election.

But Jones said the government should appeal the result. The Court of Disputed Returns could give the seat to Jones or order a new election in his electoral district.

Jones lost his seat to center-left opposition Labor Party candidate Cathy O'Toole by 37 votes after 88,337 votes were counted, then recounted.

Turnbull has confirmed that his government is considering appealing the result, but has declined to detail on what grounds.