Malcolm Turnbull will urge greater effort to improve indigenous health and education when federal parliament sits on Monday.
The prime minister and state leaders heard the views of Aboriginal and Torres Strait Islander leaders on Friday about new targets, as the 10-year-old Closing the Gap strategy struggled to meet its aims.
The targets would be "refreshed" after consultation, which had been extended to October, and Mr Turnbull will made a statement about the program's most recent outcomes on Monday.
"We have made gains, and efforts to date have improved the lives of many Aboriginal and Torres Strait Islander people, but plainly we have not been able to achieve as much success as we would like and we need to work harder," Mr Turnbull told COAG on Friday.
Former prime minister Kevin Rudd will address the National Press Club on Monday about the 10-year anniversary of his Stolen Generations apology and he said he didn't want to see Closing the Gap watered down.
"I'll be the first one leading the charge against (any watering down) by any side of politics," Mr Rudd told reporters at NSW parliament on Friday.
Two Tasmanian senators will be sworn in on Monday - one old and one new.
Devonport mayor Steve Martin will replace Jacqui Lambie, but sit as an independent after he was kicked out of her party for refusing to stand aside to let her return to the Senate.
And former tourism minister Richard Colbeck, who lost his spot thanks to a factional dispute, will return to replace his Liberal colleague Stephen Parry.
New Labor senator and former NSW premier Kristina Keneally is also set to be sworn in once NSW parliament confirms her appointment to replace Sam Dastyari.
Another new senator, the Liberals' Jim Molan, will give his first speech in parliament, while on Tuesday the full bench of the High Court will consider whether former senator Skye Kakoschke-Moore is eligible to reclaim her seat.
The government would look to push through its second round of company tax cuts, despite strong opposition from Labor and the Greens, who argued businesses are not passing on profits to workers.
"I think we are now the second highest (company tax rate) in the whole OECD," Mr Turnbull said.
"We are backing Australian businesses and Australian companies."
The Senate will debate the government's cashless welfare debit card legislation and revenge porn laws.
Labor and the Greens were set to vote against an amendment to the Murray Darling Basin Plan, as they pushed for a new review to restore confidence in the distribution of water in the region.
Reserve Bank governor Philip Lowe will be grilled by MPs on the economics committee in Sydney on Friday.
