Mr Abbott on Wednesday tabled in parliament the annual Closing the Gap statement, which assesses progress on improving all aspects of Indigenous life from health to education.
"Two centuries of occasional partial success and frequently dashed hopes has taught us that neither side of politics can achieve meaningful progress without working with the other," Mr Abbott said.
"So none of us should seek to score a point or defend a legacy here.
"Just to reach out across the aisle, because that is the only hope of lasting success."
Mr Abbott said it was important on days such as this that "we should acknowledge where we have failed".
Mr Abbott said the past year had been about developing practical reforms to address Indigenous disadvantage.
He pledged the next year would be "focused on action", including closing the gap on school attendance within five years.
But much more work was needed, the prime minister told parliament.
"Because this seventh Closing the Gap report is, in many respects, profoundly disappointing," he said.
"Despite the concerted efforts of successive governments since the first report, we are not on track to achieve most of the targets."
Mr Abbott said the government was on track to halve the gap in Year 12 attainment rates for those aged 20 to 24.
The target to halve the gap in mortality rates for Aboriginal and Torres Strait Islander children looked achievable by 2018.
The prime minister said he looked forward to reporting good results on the new target on school attendance in the years to come.
But Mr Abbott admitted other targets, including to close the gap in life expectancy within a generation, have either not been met or are not on track.
The government plans to introduce ways to improve school attendance and "break the cycle of truancy", Mr Abbott said.
Once students graduated they would need jobs, so the government will partner with Australia's largest employers to open up more employment opportunities and provide incentives to business to take on Indigenous trainees and workers.
The public sector would take on more Indigenous public servants and Indigenous small businesses would be invited to tender for government business worth an estimated $39 billion a year.
Violence in communities would be addressed through better alcohol and drug prevention and the treatment problems, improved policing and support for the victims of crime.
Mr Abbott said the government continued to work towards changing the constitution to acknowledge the contribution of Indigenous Australians.