The leader of Britain's opposition party suggested on Sunday the position should be rotated around the members.
More than 100 officers and soldiers marched in red tunics, before a 53-gun salute opened the summit.
He may be royalty but that didn't stop Prince Charles getting stuck into some Bundaberg Rum.
The Queen turns 92 on Saturday and this is expected to be the last time she attends the biennial gathering of Commonwealth leaders since she no longer travels outside the U.K. There has been some controversy about whether Prince Charles would take over when, as expected, he becomes king.
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There were also concerns Charles didn't have the strength of character required to lead the Commonwealth, with his official 1996 biography painting him as privileged and ignorant of the hardships faced by regular citizens.
"By doing so, the Commonwealth can be a cornerstone for the lives of future generations, just as it has been for so many of us".
A decision by the leaders of the member-states is reportedly to be reached by Friday.
"Australia, as you know, strongly supports the continuation of the king or queen of the United Kingdom as the head of the Commonwealth", Mr Turnbull told reporters in London on Thursday.
"You have been true to the deepest values of the Commonwealth - that the voice of the smallest member country is worth precisely as much as that of the largest; that the wealthiest and the most vulnerable stand shoulder to shoulder". The Prince of Wales "will provide solid and passionate leadership for our Commonwealth", he said.
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British Prime Minister Theresa May, the meeting's host, thanked the Queen and the Royal Family for being the Commonwealth's most steadfast and fervant champions and for nurturing the organisation.
The acceptance of Charles to be the next ceremonial head of the group "is now widely considered a foregone conclusion", The Telegraph reported, adding in a commentary that he was the "one person qualified" to succeed the queen.
Issues under discussion at the summit also include ocean conservation, cyber security, and trade between the countries. The UK is considering banning cotton buds, plastic drinking straws and single-use plastics in England starting in 2018, part of a larger campaign to halt pollution of the world's rivers and oceans.
Her intervention comes amid ongoing speculation over a successor to the monarch.
May said she would rally member states.
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