Moderate members of the Coalition are urging their colleagues to allow the process for establishing an historic Indigenous recognition referendum to move forward before rushing forward with concerns, amid division in the party room.

Meanwhile, the Labor senator Pat Dodson has said the time for obfuscation and avoidance is well past.

Craig Kelly says he could 'campaign for the no side' on Indigenous recognition Read more

“We either deliver the Uluru statement from the heart in full or continue down the failed path of soft reconciliation measures – making white folks feel like they are doing something good for blackfellas and yet doing nothing to heal the nation’s wounds and achieving unity and respect,” he wrote in an opinion piece for the Sydney Morning Herald and the Age.

Some conservative members of the Coalition have wasted no time in voicing their concerns about any future referendum before discussions begin in earnest, while others are stepping forward to try to let the matter progress unimpeded, as the party attempts to avoid reopening fractures that emerged during the marriage equality debate.

The backbench MP Craig Kelly has already flagged he could be prompted to campaign for the no side of any future referendum, if the proposal eventually put forward includes a “First Nations voice” as set out in the Uluru statementt.

In answer to some of his wary colleagues going public less than 24 hours after the minister for Indigenous Australians, Ken Wyatt, announced his intention to attempt an Indigenous recognition referendum, the backbench MP John Alexander said he was “walking with Ken”.

“We all love Australia, and we’re all supporters of improving the relationship and promoting reconciliation between Indigenous and non-Indigenous Australia; it’s how we do it that causes the problems,” he said.

“Only by walking together and engaging can we uncover pathways to a better future, I’m with Ken on this, he has my full support for the process he has initiated and I hope it can conclude with a successful referendum vote and form of ‘voice’ we can all be proud of.”

Tim Wilson said he too would be entering the discussion “with an open mind”.

“I think there is an enormous amount of goodwill to find symbolic and practical measures to help Aboriginal and Torres Strait Islanders,” the MP said.

“Wherever there is any attempt to change the Constitution, people always start wary on any topic, both because of the consequences of doing so, and the consequences of failure to meet a double majority test for it to pass.

“As someone who has seen the legitimacy of their life debated in survey form, you only take proposals forward that you are very confident are going to succeed.”

The Liberal senator Andrew Bragg told Sky News he believed the framework announced by Wyatt on Wednesday “was a good one”, which he wanted to see run its course.

“Effectively he said that the two stakeholder groups we need to get onside, are the Indigenous communities and also, the middle Australians, the quiet Australians, so he is now undertaking a co-design process to hopefully yield some form of a model which could be adopted in a referendum, and as you know, that’s pretty hard to do,” he said. “But from my point of view it sounds all very sensible.”

The former deputy prime minister turned backbencher Barnaby Joyce has taken the opportunity to reprosecute his case for increasing regional Senate representation.

“So, instead of having the majority of senators from the capital cities, there would be six regions and a program to encourage Aboriginal people, who may be more present in regional areas, to stand for those positions,” he told his local paper, the Armidale Express.

The former Nationals leader also said he believed Australians would reject any proposal which included “a third chamber of parliament” which is a mischaracterisation of the voice to parliament, an advisory panel many Indigenous people believe is crucial to reviewing legislation impacts First Nations peoples.

• Sign up to receive the top stories from Guardian Australia every morning

Wyatt used his first major speech since taking over the portfolio, delivered during Naidoc week, to call for a consensus approach to Indigenous recognition within the constitution, which he said could not move forward without taking the Uluru statement into account.

He has set a timeline of three years to work towards wording for a potential referendum on the subject, but said he would not move forward if he believed it was doomed to fail.

Dodson called for all aspects of the Uluru statement to be delivered.

“The time has come to prepare for a treaty,” he wrote. “We have a window of opportunity to get the voice designed and prescribed into law but public goodwill towards a successful referendum will not last forever. So the words to go into the constitution should be settled by the parties as soon as possible and then the question put to referendum via a unified education campaign.

“It should be done in this term of government. By the next election, we should have an agreed framework for the treaty process and begin getting the nation ready by truthtelling and constructive reconciliation actions.”