Malcolm Turnbull has sought to ease tensions with China while reminding it Australia supports the international order that respects the sovereignty of all nations.
The prime minister used a speech on international education in front of Chinese ambassador to Australia Cheng Jingye and Sydney-based consul general Gu Xiaojie to "propose clearer thinking" on the rapidly changing world.
Chinese State Councillor Wang Yi at the weekend told Australia it must do more to boost mutual trust rather than being "groundlessly suspicious".
Mr Turnbull said in the midst of rapid change, Australia would continue to advance its own interests through a relationship with China based on mutual respect and understanding.
"For our part, we act to advance Australia's prosperity, ensure the independence of decision making and secure the safety and freedom of our people," he said at the University of NSW on Tuesday.
"And in doing so, we support an international order based on the rule of law where might is not right and the sovereignty of all nations is respected by others - a principle President Xi (Jinping) endorsed when he addressed a joint sitting of the Australian parliament in November 2014."
The prime minister earlier said it would be a big mistake to assume China will assume the role of the Soviet Union in a 21st century Cold War with the United States.
"Will a stronger, richer China have a more confident and assertive voice in world affairs?" he said.
"Of course it will. Will it seek to persuade others its point of view is correct and get the best deals in trade? Of course it will, like everybody else does.
"But of course when it comes to trade, we should never forget that protectionism is self-defeating."
Ms Bishop described her meeting in Singapore with Mr Wang, China's former foreign minister, as very positive despite the "negative line" the media picked up.
"He also said there's more we can do, and I agree both Australia and China can do more to strengthen and deepen our relationship," she told Sky News on Tuesday.
The pair spoke about the use of weapons in the South China Sea, the threat posed by North Korea, and working more closely together in the Pacific during their 45-minute meeting.
Ms Bishop is looking to organise dates for a visit to Beijing, hoping to join Mr Wang on a morning run through the Chinese capital.
Relations between the two nations soured last year when Mr Turnbull accused China of meddling in Australia's affairs - a claim Beijing vehemently denied.