The current Labor Party government in Australia, which is to the left of the Liberal Party, would like to see an Australian president take over from the British monarch.
Many people regard the death of Queen Elizabeth II last week as a chance for positive transformation after she had ruled for 70 years.
The small Greens party in Victoria used their swearing-in event to call for a single Australian leader.
Greens leader Samantha Ratnam told reporters before the ceremony, "We're here as Victorian MPs to pledge allegiance to King Charles III.
Despite the protest, all four Greens lawmakers joined the rest in swearing or affirming allegiance to the king, who is head of state of Britain, Australia, and another 13 countries.
"This is a really important time to reflect on the role of the British monarchy going forward in Australia, the impact of colonisation.