Today's report - marking a decade since former prime minister Kevin Rudd made a historic apology to Aboriginal people for centuries of injustice - showed the target to halve the gap in child mortality with non-indigenous Australians by 2018 was on track to be met.
The other four targets - closing the 10-year gap in life expectancy between indigenous and non-indigenous Australians by 2031 and halving the gaps in employment, reading and numeracy and school attendance by 2018 - were all lagging.
Three of the seven Closing the Gap targets were met in the past year compared with just one a year earlier.
The only target found to be on track last year - to halve the gap in Year 12 attainment by 2020 - also remains on track.
The Closing the Gap decade has been a disappointment, with minimal improvement in the lot of Indigenous people.
But Mr Turnbull said he was waiting for an Indigenous Advisory Council to report back in April before making a decision. "One is our failure previous year, and the other is the work being done on the ground by organisations", he said.
"Too often we are quick to highlight the despondency which does nothing to help those who aspire to be like (the) people that work hard and succeed all the time, all while being proud First Australians, Aboriginal, Torres Strait Islander Australians".
"If we can not work on this together, the next Labor Government will instead - as a first step - look to legislate the voice to Parliament", Mr Shorten has told Parliament.
With three targets set to expire, the government plans to "refresh" its closing the gap strategy and decide whether targets need to be re-worked.
The new report was confirmed by Prime Minister Malcolm Turnbull to indicate advancement, even if it doesn't include all area.
The policy will extend principles of the indigenous procurement policy, which has allowed indigenous businesses to win more than $1 billion in government contracts since 2015, up from $6 million in 2012/13, he said.
"The targets we set 10 years ago for Closing the Gap between indigenous and non-indigenous Australians in health, education, employment, housing and longevity should be enhanced, not weakened", he told the National Press Club on Monday.
"Compensation is about resolving some of the unfinished business of the apology".
Mr Shorten says in the past 10-years, state Labor and Liberal governments - apart from Victoria - have established different forms of compensation for members of the Stolen Generations.