"Too often we are quick to highlight the despondency," Mr Turnbull said.
"The solution to closing the gap rests within the imagination, ingenuity, passion and drive of Indigenous people themselves."
The seven targets aim to improve Indigenous health, education and employment outcomes and were committed to by the Rudd Government in 2008.
The targets to halve the gap in Indigenous child mortality rates and Year 12 attainment as well as enrolling more children in early education are on track to be met.
But the targets to close the gap in life expectancy, employment and literacy and numeracy rates will not be met at current rates.
Shorten: Next Labor government will look to establish compensation scheme for Stolen Generation
"The last decade has given us a richer understanding of what's working and what's not," Mr Turnbull said.
The prime minister also pointed to making the states and territories more accountable for efforts to reduce disadvantage.
"State-by-state targets will give us more granular and specific local insight to progress, or lack of progress and more precisely where more focused effort is needed," he said.
The government unveiled a new Indigenous Grants Policy, which aims to increase the number of Indigenous owned and controlled organisations involved in service delivery.
"Organisations will need to demonstrate value for money and that they have the skills and expertise to deliver the grant," the Indigenous Affairs Minister Nigel Scullion said in a statement.
"Where non-Indigenous organisations are providing services, they will be required to employ local Aboriginal or Torres Strait Islander people and include local Indigenous businesses in their supply chains."
Labor commits to Stolen Generations compensation.
In his reply to the Prime Minister's address, Opposition Leader Bill Shorten committed a future Labor government to recognising an Indigenous voice to Parliament.
Following an 18-month process which culminated at the Uluru summit last May, the Uluru Statement from the Heart recommended the assembly, or "voice to Parliament", to advise the government on policies affecting Indigenous people.
Kevin Rudd slams Turnbull government on Close the Gap targets
But the government shot down the suggestions as "undesirable" and "inconsistent" with Australian democracy.
"We came to our decision after very careful consideration," Mr Turnbull told Parliament.
"The government remains absolutely committed, however, to recognising Aboriginal and Torres Strait Islander people in the Australian constitution."
The Prime Minister flagged a new parliamentary committee to reinvigorate the process.
But, the Opposition Leader said his support lay with the voice to Parliament.
"Who are we in this Parliament to simply reject it out of hand?" Mr Shorten asked the chamber.
"It's time for us to be better and braver than the path of least resistance."
Rudd: Reconciliation is achievable
The opposition leader also committed to a compensation scheme to assist survivors of the Stolen Generations.
"It's time the Commonwealth lived-up to its rhetoric," Mr Shorten said.
"To each of the survivors removed from their families, country and culture we will offer an ex gratia payment of $75,000."
The $9 million fund would be complemented by a $7.5 million National Healing Fund, which would go towards families of Stolen Generations survivors.
Labor also committed to a national summit to address the high rates of Indigenous children in out-of-home care.
There were an estimated 17,000 Indigenous children in out-of-home care last year, compared to 9,000 a decade ago.