Malcolm Turnbull has contradicted Tony Abbott’s view that the Coalition is in office but not in power on the issue of budget repair and risks abandoning its principles if it tries to govern from the sensible centre.

However the prime minister’s calls for the Labor opposition to support government policies in the 45th parliament have already been ignored. Early skirmishes on superannuation reforms and the same-sex marriage plebiscite are under way.

Turnbull appeared on ABC’s Insiders on Sunday, reiterating the key messages of a speech on Saturday that budget repair is possible if Labor and other parties cooperate in the Senate.

Turnbull rejected his predecessor Tony Abbott’s view, expressed in a speech to the Master Builders Association in Victoria on Friday, that the Coalition had been in office since 2013 “but not in power” on the issue of making budget savings.

He said if the basis for the claim was that the Coalition did not have a Senate majority, “that would suggest the only governments that have been in power in … recent times have been John Howard and Malcolm Fraser for a few years”.

“Governments normally don’t have majority in the Senate. Governments normally, historically, have to negotiate with other parties in the Senate. It has been ever thus.”

Abbott also warned the Coalition would only succeed if it continued to make the distinction between itself and Labor “crystal clear”.

“Our challenge is not to move closer to Labor in the hope of being a smaller target,” he said.

Turnbull said the government had fought for its principles, including by taking two bills for tough union watchdogs to the double-dissolution election.

“That’s fight,” he said. “That’s commitment. That’s character.”

Asked if Abbott’s message contradicted his own view that the Coalition must govern from the “sensible centre” Turnbull replied: “We are always – the Liberal party and indeed the National party – are known for a very good reason as parties of the centre right. We are centrist parties.”

Turnbull said the main goal of the next three years was budget repair because the Australian government was living beyond its means.

“One way or another, at the end of this 45th parliament, I want Australians to be able to say that … [it]has come to terms with the budgetary challenge we face and has stopped this irresponsible business of loading a mountain of debt, mountain after mountain of debt, on the shoulders of our children and grandchildren.”

He reiterated a call for Labor to pass $6.5bn of savings measures it claimed in its pre-election policy costings.

Turnbull predicted there would be a “lot of give and take” in the new parliament, but said the room for compromise between the government, opposition and other parties “remains to be seen”.

“There are 11 crossbenchers, if nine of them vote with the Coalition, that’s a majority. If Labor votes for the Coalition, that’s a majority.

“If the Greens vote with us, that’s a majority. So, what we have to do is work with the crossbenchers, work with Labor, work with the Greens and we will find the best outcome to secure our program.”

Turnbull criticised Labor’s proposed compromise on superannuation reform which remove the backdating on the $500,000 lifetime cap in return for lower thresholds for high-income contributions.

He said Labor’s proposed changes would hurt women who had been out of the workplace and people between the age of 65 and 75 who wanted to catch up using concessional contributions.

Turnbull also said Labor was opposing the government’s reform “which will enable self-employed people, independent contractors, to make concessional contributions in the same way as if they were employees”.

When host Barrie Cassidy suggested that a compromise to raise the $500,000 lifetime cap to $750,000 to quell a backbench revolt would leave the policy unsaleable, Turnbull replied this was simply his “gloomy prediction”.

He said the “vast bulk” of the proposed super reforms were accepted.

Turnbull rebuked Labor for indicating it may block the marriage equality plebiscite, saying it “must want to delay same-sex marriage for a very long time”.

At a press conference in Melbourne on Sunday the opposition leader, Bill Shorten, said Turnbull and his treasurer, Scott Morrison, were talking about cooperation but were actually seeking a blank cheque for Coalition policies.

“You cannot bully your way into cooperation – Mr Turnbull wants our cooperation on a number of matters, and we’re looking at them,” he said.

“But I’d like Mr Turnbull to tell Australians what are his trophy policies he’s willing to give up?”

Shorten targeted the government’s proposed $48bn company tax cut, resistance to a bank royal commission and Medicare policies.

“We’ll certainly be working on budget repair that is fair, we’ll certainly try and work with the government to try and improve the superannuation mess they’ve got us into,” he said.

Turnbull said reforming racial discrimination law was not a priority but did not rule out removing the prohibition on insulting or offending people based on their race.

Asked about the police raid of Parliament House over alleged leaks from NBN Co, Turnbull said it was a matter for police and the claim for parliamentary privilege over the material was a matter for the Senate.

The prime minister acknowledged the Country Liberal party had been soundly beaten in the Northern Territory election, describing it as a “landslide” and a “massive win” for the Labor party.

Turnbull said the loss was “driven overwhelmingly by local issues” and singled out disunity as the cause for defeat.