THE Federal Government will fail in its mission to close the gap on indigenous disadvantage unless it fixes the education system, former Labor prime minister Kevin Rudd will tell an Adelaide crowd today.

It is the second time Mr Rudd has criticised government policy in two days.

He will use the fifth anniversary of his apology to the Stolen Generations to call on the Government to add a seventh item to its Closing the Gap targets, and "close the gap in vocational and higher education".

Mr Rudd grabbed headlines yesterday when he said Prime Minister Julia Gillard and Treasurer Wayne Swan had to take responsibility for the mining tax, which has netted just $126 million in its first two quarters, a fraction of the $2 billion it was expected to raise.

Today, he will outline the "gaps and cracks" throughout the education system and challenge the Gillard Government to fix them in its response to the Gonski review of school funding.

Mr Rudd has failed to end speculation he would have another tilt at the Labor leadership and his thinly veiled criticism of the Gillard Government is unlikely to help.

Last week, Ms Gillard said Australia was on track with some Closing the Gap targets - such as indigenous employment and infant mortality - but conceded the Government would struggle to meet others, particularly literacy and numeracy and life expectancy targets.

Mr Rudd challenged them to do more.

"(If) we don't have a system that accommodates a full education experience then we will fail," Mr Rudd will tell a Reconciliation SA breakfast this morning. He will highlight low indigenous university enrolments and completion rates, and other indicators of disadvantage.

"I note that the Review of Funding for Schooling (Gonski review) found that apart from those students who did not speak English, indigenous students are the most developmentally vulnerable in our education system," he said. "I believe we need to add a seventh target to our Closing the Gap targets, that is to close the gap in vocational and higher education."

After Mr Rudd was toppled by Ms Gillard in June 2010, he highlighted the apology as one of his proudest moments.

Ms Gillard made restarting Mr Rudd's failed mining tax negotiations a priority but Mr Rudd said yesterday that in its final form the tax had "not collected any real revenue".