Abbott also needs Senate support to fulfill his promises to repeal a deeply unpopular carbon tax on Australia's biggest industrial polluters and a 30 percent tax on coal and iron ore miners' profits.
One of the biggest former donors to Abbott's coalition, eccentric mining magnate Clive Palmer, withdrew his patronage to bankroll his own political party, Palmer United Party.
Palmer, who is building a replica of the ocean liner Titanic â¿¿ which will be named Titianic II and make its maiden voyage in 2016 â¿¿ is close to winning his own seat in the House of Representatives. A Palmer United Party senate candidate, former football star Glenn Lazarus, looks even more likely in his home state of Queensland.
Abbott's new government wants to discuss with Indonesia plans to have the Australian navy turn back Indonesian fishing boats carrying asylum seekers into Australian waters. The coalition has proposed that the government buy old fishing boats from Indonesian fishermen to prevent them falling into the hands of people smugglers.
Labor argued that both policies could damage Australia's relations with Indonesia, its closest neighbor after Papua New Guinea.
Saturday's election likely brought Australia's first Aboriginal woman to Parliament. Former Olympian Nova Peris is almost certain to win a Senate seat for Labor in the Northern Territory, but the final results will not be known for days.
WikiLeaks founder Julian Assange's bid for a Senate seat in Victoria state appeared doomed on Sunday.
His Senate running mate for the newly founded WikiLeaks Party, Binoy Kampmark, said the secrets spiller was unlikely to win a seat after attracting just a little more than 1 percent of the votes in Victoria. The Senate count won't be finalized for days.
Assange, who is hiding out in the Ecuadorean Embassy in London in a bid to avoid extradition to Sweden on sex crime allegations, told the Australian Broadcasting Corp. that he was happy with the party's performance, and is likely to run again.