Federal parliament resumes this week and debate will begin on the savings package, which contains 26 savings measures the government argues Labor indicated it would adopt during the election campaign.

Labor has partly disputed that claim, arguing its election policies did not explicitly commit to a $1 billion cut to the renewable energy agency ARENA, nor to a $1.3 billion cut to the clean energy supplement, originally linked to the axed carbon tax, which would actually deliver a cut in real terms to the incomes of Newstart recipients.

A rearguard action has been underway within Labor, publicly led by shadow cabinet minister Anthony Albanese and backed by welfare groups such as ACOSS, to oppose the cut to the supplement and, behind the scenes, the government and opposition have been negotiating over a way to find alternative savings.

Mr Morrison told Fairfax Media on Sunday that, since the bill had been introduced to the Parliament, discussions over a compromise deal had been "constructive".

"As we return to the Parliament, in this week and the weeks that follow, it is necessary for Labor to now follow through on those discussions," he said.

"The fact remains that the task of arresting the debt requires the opposition to, at the very least, support savings measures that they themselves committed to before the last election.

"We welcome their engagement, as with members of the crossbench parties, and we will continue to stay focused on the job of getting the results the Australian people expect."

Labor treasury spokesman Chris Bowen told Fairfax Media the party would "have more to say when we have been through our normal internal processes".

If a deal is done to pass the $6 billion savings package in the coming weeks, it will represent a win for the Treasurer and a significant boost to Prime Minister Malcolm Turnbull's flagging fortunes at the one year anniversary of his ascent to the prime ministership.

Labor sources familiar with the negotiations confirmed a deal was being hammered out that would allow Newstart recipients to keep their energy supplement payments, which are worth just $5 a week.

"[Opposition Leader] Bill [Shorten] has been concerned that low-income earners would get hit if the supplement is cut, particularly as higher income earners would not be affected," said one insider.

"Bill, Jenny [Macklin] and [Chris] Bowen have been working on this and both sides are being pragmatic."

If a deal is done, savings will be found elsewhere to make up for the forgone revenue. It is less clear, however, if the cut to ARENA will be blocked.

Labor's shadow cabinet is expected to discuss the matter – and finalise its position – before taking it to Tuesday morning's caucus meeting for debate. Opponents of the cut to the supplement point out it was not approved by shadow cabinet during the election campaign and they only now have had a chance to debate it.

Earlier on Sunday, former prime minister John Howard urged his successor to work harder to unite the party and tackle industrial relations and tax reform.

Mr Howard said Mr Turnbull, who will mark his one year anniversary as prime minister this week, could run a successful government but must work to unite his team.

"There's no reason why Malcolm Turnbull can't lead the government through to the next election and do it successfully," Mr Howard said.

"He has to unite the party behind a clear economic and political program.

"At some point we have to return in earnest to change and reform in the areas of taxation and industrial relations, you can't avoid that," he told Sky News.

"The fact these are difficult doesn't mean you don't try them. I don't buy the idea you can't go back to the reform marketplace any more."

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