Malcolm Turnbull has said the government will present the bill to reinstate a tougher building industry watchdog to a joint sitting of parliament, despite a cabinet minister declaring the bill’s prospects are dead.

On Tuesday Turnbull explained the reason he had called a double-dissolution election was “not related to the composition of the Senate” but rather because it was “the only way” to pass two industrial relations bills to crack down on union misconduct.

The Australian Building and Construction Commission and the registered organisations legislation, which would reinstate the tougher building industry watchdog and increase penalties for industrial law breaches, were rejected at a special sitting of parliament in April.

Turnbull said the procedure of calling a double dissolution and holding a joint sitting of the two houses of parliament was “literally the only option we had other than saying we give up and we will just wait until some remarkable day when there is a majority in the Senate”.

“We had and have the courage of our convictions and we will, if we return to government as I’m confident we will, we will re-present those bills in accordance with [the constitutional section dealing with joint sittings].”

On the ABC’s Q&A on Monday the resources and energy minister, Josh Frydenberg, claimed the ABCC would improve productivity and explained it had been part of the platform in 2013.

Tony Jones asked if the ABCC bill was dead and Frydenberg conceded “it’s going to be dead, because of the Labor opposition”.

On Sunday, Frydenberg told ABC’s Insiders the government did not have the numbers to pass either of the bills.

Frydenberg said Turnbull had “put his best foot forward and obviously we are not going to get the numbers in the double dissolution but those issues are very important”.

In the election campaign, Turnbull had said restoring the ABCC would help stop “excessive” pay rises like the Construction Forestry Mining Energy Union’s (CFMEU) Victorian branch’s deal for a 15% pay rise over three years in the construction sector.

On 2 July in a fiery speech as election results produced an inconclusive result, Turnbull said the government could not “let the CFMEU get on with doing what they like and never challenge them”.

Re-elected lower house MPs Bob Katter, Andrew Wilkie and the Greens’ Adam Bandt all voted with Labor to abolish the ABCC in 2012 and are not expected to endorse its return at a joint sitting.

Tasmanian senator Jacqui Lambie, who was re-elected on Saturday, voted against the ABCC bill in April.

Nick Xenophon, who was re-elected and will have three senators in the new parliament, voted in favour of the second reading to allow debate to proceed but proposed amendments on health and safety.

Although the final makeup of the Senate and House of Representatives is not known, the opposition of Labor, the Greens, and those crossbenchers is believed to be sufficient to defeat the bills.

Derryn Hinch, who is likely to be elected as a senator in Victoria, has said he is unsure whether he will support the ABCC bill.