Malcolm Turnbull has likened building union "thuggery" to "something scripted for the Godfather" as the coalition used its numbers to push through bills to reinstate the building watchdog.

In an unusual move, the prime minister summed up truncated debate on bills to re-establish the Australian Building and Construction Commission.

The bill passed the lower house by 76 to 69 on Tuesday.

Mr Turnbull used video of a construction union official’s threatening behaviour on a Commonwealth Games building site on the Gold Coast to bolster his case.

“Not content with a tirade of foul-mouthed abuse, this representative of the CEFMU goes on to make one of those menacing threats that none of us would ever wish to hear,” Mr Turnbull told parliament.

“‘I have your phone number. I know where you live’.

“This is not something scripted for the Godfather or the Sopranos, this is the practical reality of life on a construction site in our country.”

Earlier the coalition used its numbers to suspend usual business of parliament and bring on gagged debate on the bill, which was used to trigger July’s double dissolution election.

Leader of the House Christopher Pyne argued the views of everyone in the chamber had been documented in the previous two attempts to pass the legislation.

But Labor hit back, accusing the government of forgetting the newly elected members who should get their say.

“If the government thought the debate was going well for them, they would not be moving this motion,” manager of opposition business Tony Burke told parliament.

Mr Turnbull believes there’s no doubt his government has a mandate for the legislation after being reinstalled in July.

“And those opposite will be showing their contempt for that democratic outcome if they persist in the obstruction of these bills,” he said.

“We all know criminality is rife in this sector.”

The prime minister is convinced union officials treat “very small” fines imposed on them for misconduct as no more than parking fines.

But Labor frontbencher Mark Dreyfus insists the construction industry already has massive oversight from rigorous laws.

“Basically, it seems part of this government’s anti-worker, anti-union agenda,” he told reporters.

The bill now heads to the Senate, where the numbers are unclear.

The coalition is negotiating with crossbench senators, including Liberal Democrat David Leyonhjelm, who wants a relaxation of a ban on lever-action Adler shotguns in exchange for his support.

Mr Turnbull has discussed the issue with him personally but told the ABC firearms regulation was a matter for the Council of Australian Governments.

Independent senator Nick Xenophon – who leads a team of three – argued the construction watchdog would not be credible unless it also dealt with the plight of subcontractors when building contractors collapsed.