The former coalition MP, who lost his seat at the last election, said he had taken a report to cabinet on two separate occasions while he was in office on what an Indigenous voice would look like.
Mr Wyatt said the argument used by Nationals MPs that they did not have enough detail about the voice was only being used as an excuse for not backing the referendum.
"To my mind, it offers up a level of immaturity around a very complex issue," he told ABC Radio on Wednesday.
"What is obvious with the National Party is they have not read the report and have not given an Aboriginal voice to Parliament an opportunity to be aired, and to be listened to and to be implemented."
While Nationals leader David Littleproud said the voice would not deliver practical outcomes for Indigenous people, Mr Wyatt said he was extremely disappointed with the party's stance.
"I challenge every federal member to get out of their offices, go to the Aboriginal organisations within their electorates, sit and listen to the issues, see firsthand what Aboriginal people are talking about," he said.
"I'm not hearing from the Nationals solutions to the complexities of the problems that still sit there with Aboriginal people on the ground."
The comments coincide with the handing down of the 2022 Closing the Gap report to parliament on Wednesday, which shows many of the key targets are not on track.
It will be the first report since the national agreement on Closing the Gap took effect.
In 2020, an agreement between the federal government, the Coalition of Peaks, all state and territory governments and the Australian Local Government Association (ALGA) was struck and aimed to renew ways of working together to improve outcomes for Indigenous Australians.
The groups agreed to improving 18 socio-economic outcomes across health, education, employment, housing, justice, safety, land and waters, culture, language and connectivity.
But two years later only four of the targets are currently on track, while four are getting worse and others have insufficient data to assess their progress.
Worsening targets include the number of children who are school-ready, adult incarcerations, children in out-of-home care and deaths by suicide.
Targets currently on track are the number of babies born at a healthy weight and children enrolled in pre-school.
The Minister for Indigenous Australians, Linda Burney, said the latest annual report told a story of mixed success, and that is was disappointing to see a lack of progress in a number of areas.
"The Closing the Gap architecture can only work when all parties are invested and there is a coordinated effort from all jurisdictions in partnership with First Nations peoples," she said.
"We have to work more closely with Aboriginal and Torres Strait Islander people to make real and much needed progress."
Senator Malarndirri McCarthy - assistant minister for Indigenous Australians and Indigenous Health - said slow progress on the targets was "understandably frustrating" to so many First Nations communities and organisations.
"Any single person taking their life is a tragedy, but the rates of suicide in First Nations communities are alarming and a serious indication of the amount of work that needs to be done to support people and their wellbeing," she said.
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