Prime Minister Tony Abbott has told Chinese President Xi Jinping of his "fervent hope" that ties between the two nations can be strengthened.
Mr Abbott met with the Chinese leader for the first time just hours after arriving in Bali on Sunday evening ahead of the annual APEC leaders summit.
Trade was top of Mr Abbott's agenda for his meeting with one of the world's most powerful men. He wants to revitalise long-running free trade negotiations with China.
Mr Abbott told Mr Xi it was an "honour" to meet him, before saying he wanted to make two key points.
"First to say that China's strength, China's growing strength, is a benefit to the world, not a challenge," Mr Abbott said.
"Certainly we in Australia owe much of our prosperity to rapidly growing trade relations between our two countries.
"The other point I'd make Mr President is that we have a strong relationship and it's my fervent hope it will become even stronger in the months and years ahead."
Mr Xi congratulated Mr Abbott on his recent election win.
"Mr Prime Minister, I appreciate your positive attitude on growing the China-Australia relationship," the Chinese leader said through an interpreter.
"I also firmly believe that as important countries in the Asia Pacific region, China and Australia entering into closer cooperation not only serves the interests of both our countries but will also add positive energy to the region."
The prime minister is also expected to meet with the leaders of Papua New Guinea, Singapore, Thailand, Malaysia, Canada and Mexico on the summit's sidelines in the coming days.
But a planned meeting with Barack Obama was cancelled after the US president decided to stay in Washington to deal with the ongoing government shutdown.
Trade is top of Mr Abbott's to do list, particularly the ambitious Trans-Pacific Partnership (TPP) negotiations, which seek to establish a grand free trade area that would include Australia and 11 other Asia-Pacific nations. But there are doubts about whether the TPP talks will be able to make much progress without Mr Obama.
APEC wraps up on Tuesday, and Mr Abbott will head to the tiny sultanate of Brunei for what's known as the East Asia Summit on Wednesday.
It brings together the leaders of the 10 ASEAN South-East Asian nations, plus Australia, New Zealand, the US, Russia, China, India, Japan and South Korea.
Mr Abbott returns to Australia on Thursday.
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