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Australian Republic Movement Chair Peter Fitzsimons seized on comments from Mr Turnbull on Monday, suggesting a postal vote or plebiscite for assessing public opinion on the issue of breaking from the monarchy.
"I think the first thing you'd need to do is to have an honest open discussion about how a president would be elected," Mr Turnbull told reporters.
"You've got to have that discussion and it may be a plebiscite.
"Maybe even a postal survey, given the success of the marriage postal survey, could be one way to deal with that."
Mr Fitzsimons urged Mr Turnbull to hold a public vote on the issue during the next parliament.