Speaking after the national citizenship ceremony in Canberra, Mr Turnbull said there has to be a sense that the time is right.
"There are many more urgent issues confronting Australia and indeed confronting the government than the momentum or the desire for Australia to become a republic," he told reporters on Australia Day.
Mr Turnbull, the former head of the Australian Republican Movement, said he took the view after the 1999 referendum defeat that the best time to try again would be after the end of the Queen's reign.
"I have led a `yes' case for a republic into a heroic defeat once, I have no desire to do so again," he said.
"What we will have to see is whether there is enough popular momentum, whether it becomes a front of house issue."
During his time leading the movement he learnt momentum needs to be built through grass-roots support.
"I can't stress enough that this is a decision for the Australian people," he said.
The prime minister welcomed support for the issue and said the government would obviously monitor the strength of the push.
"I have no doubt in the future there will be another referendum and the matter will be decided as it should be by the Australian people, but the timing of that referendum has to be right."
Opposition Leader Bill Shorten has challenged Mr Turnbull to "seize this moment" in the push for Australia to become a republic, after state and territory leaders declared their support.
Mr Shorten said he recognised that Mr Turnbull was "badly bruised" after the 1999 campaign, but now was the time for the pair to work together.
"I call upon Malcolm Turnbull to stand up for what he believes in," he told reporters in Melbourne.
The Labor leader said never before has there been such important consensus between the nation's political leaders.
