The global community had engaged with China to help it grow but now must demand the world's second-largest economy bring more transparency to its trade relationships and take a greater share of the responsibility for addressing climate change, Morrison said.
"The world's global institutions must adjust their settings for China, in recognition of this new status," said Morrison in a speech to the Chicago Council on Global Affairs, referring to China as a "newly developed economy".
"That means more will be expected of course, as has always been the case for nations like the US who've always had this standing," Morrison said in the speech, according to a transcript provided to Reuters.
Global trade rules were "no longer fit for purpose" and in some cases were "designed for a completely different economy in another era, one that simply doesn't exist any more", he added.
Referring to China as a newly developed economy marks a change from Beijing's self-declared status as a developing economy, which affords it concessions such as longer times to implement agreed commitments, according to the World Trade Organization (WTO).
It also puts Australia into line with a campaign led by US President Donald Trump to remove China's developing-nation status. In an April 7, 2018 tweet, Trump wrote that China was a "great economic power" but received "tremendous perks and advantages, especially over the US".
Trump said in July 2019 that the WTO should strip China of its developing-nation status.
The World Bank classifies China as an "upper-middle-income" economy, with an annual per capita income of $3,996 to $12,375. The bank puts China in the same category as 59 other economies, including Albania, Brazil, Cuba, Gabon, Sri Lanka and Malaysia. The US is categorised among "high-income" economies with a per capita income of $12,376 or more.
Morrison has previously urged China to reform its economy and end a trade war with the US but has until now stopped short of taking a public position on its WTO status.
While two-way trade between Australia and China has grown since the countries signed a trade pact in 2015, increasing to a record 183 billion Australian dollars ($127bn) last year, the bilateral relationship has at times been strained.
In December 2017, former Australian prime minister Malcolm Turnbull accused China of meddling in its domestic affairs. The relationship was further soured by Canberra’s decision last year to effectively ban Chinese telecoms firm Huawei Technologies from its 5G broadband network rollout.
Morrison said Australia and the US had different relationships with China, given Australia had a trade surplus with China while the US had a trade deficit.
"The engagement with China has been enormously beneficial to our country," he said. "We want to see that continue."