Malcolm Turnbull says the next push for a republic in Australia must be driven by a grassroots movement rather than be imposed by politicians or the campaign will end in another “heroic defeat”.

The prime minister, an avowed republican who led the “yes” campaign before the 1999 referendum, gave this assessment after the newly announced Australian of the Year, David Morrison, pledged support for constitutional change.

The Australian Republican Movement has sought to build momentum by publishing a pro-republic open letter from all premiers and chief ministers, with the exception of Western Australia’s Colin Barnett, and the federal opposition leader, Bill Shorten, has said the “stars are aligning” for another debate.

Turnbull said he welcomed the additional voices of support and the government would monitor the strength of that support. But he suggested it was up to the proponents to show the push for a republic was a genuine popular movement because it would fail if seen to be government-driven.

“No politician, no prime minister or opposition leader or premier, can make Australia a republic. Only the Australian people can do that through a referendum,” he said after hosting an Australia Day citizenship ceremony in Canberra.

“There needs to be very strong popular momentum for a change. 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.”

I have led a yes case for a republic into a heroic defeat once. I have got no desire to do so again Malcolm Turnbull

Turnbull said he had formed the view after the 1999 vote that the next referendum should be held after the end of the Queen’s reign to have the best chance of succeeding. He still held that view.

“One of the things I have learnt from being chairman of the republican movement in the past is that if the move to a republic is seen as being politically driven, being driven from the top down, then it won’t succeed,” he said.

“To get momentum – and frankly there was more momentum in the late 90s than there is now – it needs to have grassroots support. It is not something that a government can just do, even if it wanted to.

“I have led a yes case for a republic into a heroic defeat once. I have got no desire to do so again. If you really are committed to Australia becoming a republic, then you want to be sure that the manner and the timing of the referendum is such that it is successful and that it unites rather than divides Australians.”

Shorten said he understood Turnbull had been “badly bruised” by the failure of the 1999 campaign, but the prime minister needed to “shed the ghosts of the past generation, and indeed Tony Abbott and the right wing of his Liberal party”.

The Labor leader said the lesson from 1999 was that it cannot be “a politicians’ republic”. That meant it would be sensible to test public opinion by the use of a plebiscite – a non-binding vote – before moving to a referendum.

“The stars are aligning for a debate about Australia becoming a republic,” Shorten said on Tuesday.

“Now is the time. We have such political consensus. I offer bipartisanship to Malcolm Turnbull. Let us together make Australia a country where at least one qualification to be head of state is that you’re an Australian citizen.”

Shorten did not believe the country should wait until the death of the monarch.

“In many ways, if we were to prepare the process to becoming a republic, that would actually immortalise Queen Elizabeth II’s reign as an excellent monarch, the longest-serving monarch in British history, and it would be a fitting end to her time if then we seamlessly move to become a republic,” he said.

Morrison, the former army chief who was recognised for gender equality, diversity and inclusion, used his Australian of the Year acceptance speech to rally support.

“It is time, I think, to at least revisit the question, so that we can stand both free and fully independent amongst the community of nations,” he said on Monday evening.