Abbott met with bureaucrats to go over his border security plans and said his first priority would be to repeal the deeply unpopular carbon tax on Australia's biggest industrial polluters.
Abbott's conservative Liberal party-led coalition won a crushing victory in elections Saturday against the center-left Labor Party, which had ruled for six years, including during the turbulent global financial crisis. Labor was ultimately doomed by years of party instability and bickering, and by its decision to renege on an election promise by implementing the carbon tax, which many Australians blame for steep increases in their power bills.
The Australian Electoral Commission's latest count Sunday had the coalition likely to win a clear majority of 86 seats in the 150-seat House of Representatives. Labor appeared likely to secure 57.
In an open letter Sunday, Abbott said he would immediately implement his border protection plan, under which the Australian navy would turn back Indonesian fishing boats carrying asylum seekers into Australian waters. The coalition has also proposed that the government buy old fishing boats from Indonesian fishermen to prevent them from falling into the hands of people smugglers.
Labor has dismissed the boat-buying policy as "crazy," and the idea was sharply criticized on Sunday by Mahfudz Siddiq, a senior Indonesian lawmaker, who said it would threaten relations between the two countries.
"His idea is clearly insulting the dignity of Indonesians," he said. "It showed to us that he does not understand diplomacy."
Abbott, a supremely fit 55-year-old, began his first day as prime minister-elect with an early morning bicycle ride from his Sydney home with friends.
"It was a very big night, but this is just the start of another normal day and there's going to be a fair bit of solid work this morning," Abbott told reporters. "There's a lot of work that will be done later today."
In his letter, Abbott took a dig at the outgoing Labor government's notorious infighting.
"We will be a careful, collegial, consultative, straight-forward government that says what it means and does what it says and that does not waste your money," Abbott wrote.
Abbott also held briefings Sunday with defense and intelligence officials to get an update on the Syrian civil war. Abbott, whose party is often criticized for placing too little value on foreign relations, caught heat last week for describing the Syrian crisis in an interview as "baddies versus baddies." Outgoing Prime Minister Kevin Rudd dubbed the comments "the most simplistic analysis I've ever heard."
The coalition has made clear that it intends to make steep cuts to spending in a bid to return the Australian budget to a surplus after five consecutive deficits delivered by Labor since the global economic crisis.
Last week, the party announced that if elected it would plan to save 4.5 billion Australian dollars ($4.1 billion) over the next four years by reducing increases in its aid spending to the Australian inflation rate, which is currently less than 3 percent. The money saved will be reallocated to fund road projects.
The outgoing Labor government said in May that Australia's long-standing pledge to increase its foreign aid spending to 0.5 percent of gross national income by 2015-16 would be postponed by two years.
The coalition said in a statement last week that it shared Labor's commitment to reach the 0.5 percent target "over time, but cannot commit to a date given the current state of the federal budget."
"I have to say, there are higher immediate priorities" than reaching the 0.5 percent target, Abbott told reporters last week. "The best thing we can do for our country and ultimately the best thing we can do for people around the world is to strengthen our economy."
The plans have been condemned by opponents and aid groups, who dubbed it short-sighted and contrary to the nation's image of global cooperation, particularly in light of Australia's recent appointments to presidency of the U.N. Security Council and the G-20 in 2014.
The coalition appears unlikely to win a majority in the Senate. But the election could deliver some conservative-minded senators for minor parties that Abbott could deal with.
Abbott also needs Senate support to fulfill his promises to repeal the carbon tax and a 30 percent tax on coal and iron ore miners' profits.
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.
Associated Press writers Kristen Gelineau in Sydney and Niniek Karmini in Jakarta, Indonesia, contributed to this report.