"This virus has inflicted a calamity on our world and its peoples. We must do all we can to understand what happened for no other purpose than to prevent it from happening again."
The inquiry resolution backed by 145 countries in May does not mention China, instead committing to an impartial, independent and comprehensive evaluation of the pandemic.
China eventually supported the European Union motion.
Ties between the two nations have since been fraught, with tariffs being imposed on some goods and Australian journalists being evacuated from China.
Mr Morrison urged other leaders to share a coronavirus vaccine if they discover one, as the United States resists global efforts to collaborate on a vaccine.
Scott Morrison urges sharing of COVID-19 vaccine
He has previously said if Australia found a vaccine, it would be shared across the world.
"When it comes to a vaccine, Australia's view is very clear - whoever finds the vaccine must share it," Mr Morrison said.
"This is a global responsibility and it's a moral responsibility for a vaccine to be shared far and wide.
"Some might see short-term advantage or even profit, but I assure you, to anyone who may think along those lines - humanity will have a very long memory and be a very, very severe judge."
Mr Morrison's speech also focused on the dangers of disinformation, urging for more to be done to prevent it.
"Disinformation costs lives and creates a climate of fear and division," he said.
"It goes against Australia's values and beliefs as a free, open society."
The prime minister also touched on trade rules and the need to peacefully resolve disputes through dialogue.
"As an outward-looking, sovereign, trading nation, Australia also values the rules and institutions that enable international trade," Mr Morrison said.
"We know that trade creates wealth and brings nations together. It makes us more prosperous, all of us.
"We won't retreat into the downward spiral of protectionism in Australia."
Mr Morrison says Australia is leading efforts to reform the World Trade Organisation to create non-discriminatory trade rules as well as a digital guide.
"We need to make sure these standards serve all countries rather than any single power and that they are developed in line with the fundamental principles of the global order."
On reform of the UN itself, Mr Morrison said Australia wanted to see multilateral institutions deliver "for us and all nations".
"We're committed to ensuring they are fit for purpose, that they're effective, that they're open and transparent and, most importantly, that they are accountable to the sovereign states that form them."
People in Australia must stay at least 1.5 metres away from others. Check your state’s restrictions on gathering limits. If you are experiencing cold or flu symptoms, stay home and arrange a test by calling your doctor or contact the Coronavirus Health Information Hotline on 1800 020 080. News and information is available in 63 languages at https://sbs.com.au/coronavirus
With additional reporting by AFP.