Tony Abbott has the opportunity to be a force for good in the upcoming election campaign, his successor Malcolm Turnbull says, just hours after the former prime minister claimed Turnbull would largely be campaigning on his government’s policies.

Abbott was ousted from the prime ministership in September, but told Sky News on Monday night that his legacy lived on.

“The Turnbull government is seeking election fundamentally on the record of the Abbott government. Stopping the boats, finalising the free trade agreements, our strong national security policy,” he said.

“It’s very easy for me to campaign on the election of a Turnbull government because the Turnbull government is running on the Abbott government’s record. It’s a very strong record.”

Turnbull told Macquarie Radio on Tuesday that Abbott’s input to the upcoming election campaign could boost the government or tear it down.

“It depends on what he says, frankly. Whether it’s a plus or minus depends entirely on the nature of his contribution,” he said. “I hope that he will be supportive and he’s indicating that he will be, so that will be good.”

Turnbull said there were policy similarities between the leaders, but “many areas of change” too.

“There are many policies that have been announced and many initiatives that have been undertaken that were either not policies or not being pursued by Mr Abbott.”

VIDEO (click or tap image to play): Tony Abbott speaks to Sky News from London on Monday evening. Source: Sky News Australia VIDEO (click or tap image to play): Tony Abbott speaks to Sky News from London on Monday evening. Source: Sky News Australia

The employment minister, Michaelia Cash, issued a veiled threat to members of the Coalition rightwing who were considering agitating for Abbott’s return.

“I know what my goal is and I would hope that would be the goal of all members of the Liberal party and that is to ensure the re-election of the Turnbull government,” she told ABC TV.

“Malcolm Turnbull was a senior cabinet minister in the former Abbott government. Clearly we have a continuation of policies. So we will be campaigning on Coalition government policies. But we’ll also be campaigning on the agenda of the Turnbull government.”

Turnbull lists Senate voting changes and changes to media laws, as well as his innovation agenda, as ways in which his government differs from his predecessor’s.

But he would not be drawn on his economic policy.

“There will be important changes in terms of tax but you will have to wait until 3 May for the budget,” he tells ABC Radio.

On Monday, Turnbull issued a directive to the Senate crossbench to pass two stalled pieces of industrial relations laws or face a 2 July double dissolution election.

Turnbull pushed the case for industrial relations changes, saying bringing corrupt unions into line will benefit workers in the construction industry as well as members of trade unions more broadly.

“Union membership is declining and one of the reasons it is declining is because people don’t have confidence in the unions,” the prime minister said. “Our laws will improve the standing, the reputation, the integrity of unions.”

The government is putting the hard word on Senate crossbenchers to pass legislation relating to the establishment of the Australian building and construction commission (ABCC) – a bill it has already been rejected once – and the twice rejected registered organisation bill, which would crack down on union governance.

“We hoped that after the Heydon royal commission’s findings came down – and they were so, so compelling, so clear – that this type of legislation was required and recommended, we hoped that that would persuade the crossbenchers to support these bills,” Turnbull said.

Labor will not support the re-establishment of the ABCC.

“Labor won’t be supporting the government’s measures. So, I suspect in fact, I am pretty sure, we will be having an election on 2 July in 103 days time,” the opposition leader, Bill Shorten, told Channel 7’s Sunrise program.

Without the support of Labor or the Greens – who have also rejected the legislation – the government needs six of the eight crossbenchers to pass it.

So far only one, Family First senator Bob Day, has thrown their support behind it, strongly signalling the government will go to a double dissolution election.

Independent senator Jacqui Lambie on Monday night confirmed that she would be shooting it down, too.

“I will be voting no to the ABCC,” she said on the ABC’s Q&A program. “I will be quite honest, I will not be blackmailed, I will not have a gun held to my head. That is not the way to play politics.”

Several other crossbenchers want far-reaching amendments to the ABCC legislation, including the formation of a national anti-corruption body, similar to New South Wales’ Independent Commission Against Corruption (Icac).

The government wouldn’t buy that, Cash confirmed.

“I have not said I won’t accept amendments. I’ve said I will negotiate in good faith but I will not accept amendments that will change the fundamental integrity of the bill. An example is it’s been put to me we should get rid of the ABCC proposal and bring in a federal Icac. It completely and utterly changes the legislation. That is not something the government is able to consider,” she said.

The stand-off effectively kicks off a 15-week election campaign.

“What Mr Turnbull has done is confirmed what many of us have confirmed for a while, that the election will be after a 103-day campaign,” Shorten said.

The prime minister on Monday recalled both houses of parliament on 18 April to pass the two industrial relations bills, and brought the budget forward to 3 May.