Prime Minister Tony Abbott says he will use 2014 to start a "conversation" about recognising Indigenous Australians in the constitution.

The former Labor government shelved plans for a referendum on the issue because it argued there was not enough community support.

Mr Abbott has used his New Year's Day message to flag that he will make garnering support a key priority for this year.

"I will also start the conversation about a constitutional referendum to recognise the first Australians," he said.

"This would complete our constitution rather than change it."

Deputy Liberal leader Julie Bishop acknowledges Australians do not make alterations to the constitution lightly.

"The Labor Party had a desultory attempt on this but they didn't engage in a deep discussion with the Australian people," she said.

Mr Abbott's intention has been welcomed by Warren Mundine, the head of the Prime Minister's Indigenous Advisory Council.

But he says more debate will be needed to build a strong case for change.

"For it to be successful, the proposed wording will need to be right," he said.

"It's not only just about the majority of people supporting it, but you have to get a majority of states.

"That double whammy makes it a bit more difficult, so I suggest caution.

"But at the same time I think we just need to get on with the job and start getting the wording right."

Acting Greens leader Richard Di Natale says Mr Abbott's announcement is encouraging.

"The rhetoric from Tony Abbott is good. I'm worried that he won't follow through so we'll be holding him to account on that," he said.

The Government has promised to put forward a draft amendment by September but has not set a timeframe for a referendum.