Turnbull, a multi-millionaire former banker, was sworn in on Tuesday in a simple ceremony officiated by Australia's governor-general at Government House in Canberra, less than 24 hours after he challenged Abbott for the top job.

Ahead of the ceremony, Turnbull told reporters he would focus on stability and set about improving the faltering economy.

"I'm filled with optimism and we will be setting out in the weeks ahead... more of those foundations that will ensure our prosperity in the years ahead," he said.

The former communications minister assured Australians that the government remained strong despite becoming the nation's fourth leader in just over two years after an internal party revolt.

60-year-old Turnbull assumed office as the country's 29th prime minister after a surprise ballot of his conservative Liberal Party gave him 54 votes vs. 44 for Abbott, who was elected to office barely two years ago.

Turnbull's elevation to the prime minister's office comes after the party's popularity plummeted under Abbott's leadership, which was often seen as combative and divisive.

He oversaw the faltering of Australia's record economic boom - 25 years of continuous growth - and faced tough criticism over a series of unpopular policies.

In his first speech since his ouster, Abbott warned that the ongoing volatility in the government could hurt the nation's standing on the global stage.

"Australia has a role to play in the struggles of the wider world: the cauldron of the Middle East and security in the South China Sea and elsewhere," he told reporters. "I fear that none of this will be helped if the leadership instability that's plagued other countries continues to taint us."

But Abbott promised not to destabilize the new prime minister, without adding whether he would quit politics. But he did single out the "sour, bitter character assassination" he had received in the Australian media, leading to his second leadership challenge in seven months.

Until now, Turnbull's progressive views on climate change, same-sex marriage and a desire to make Australia a republic, had limited his chances of leading the party.

But many senior Liberal members and political analysts agree that he is now a stronger candidate to take on the opposition Labor party in elections, due in about a year.

"If the election was held yesterday (Monday), the opposition would have won. If it was held today they would lose," said Peter Chen, a senior lecturer in government at Sydney University.

Turnbull is expected to make a major cabinet reshuffle in the coming days.

mm/jil (AFP, AP, Reuters)