The Federal Government will keep fighting to bring back the workplace cop - the Australian Building and Construction Commission (ABCC) - after failing to reintroduce it this week.

Labor, the Greens and a number of crossbenchers voted against the construction watchdog's return in the Senate.

The Government won support from crossbench senators Bob Day, David Leyonhjelm, John Madigan and Nick Xenophon to move on to the next stage of debate, but three other crossbenchers – Jacqui Lambie, Glenn Lazarus and Ricky Muir – sided with Labor and the Greens to block the move.

Meanwhile, Palmer United party senator Dio Wang abstained.

Still, Employment Minister Eric Abetz has continued to insist that the ABCC is needed.

“For too long, there has not been a deterrent in the construction industry for doing the wrong thing,” Senator Abetz told reporters after the vote.

“A re-established ABCC is aimed at changing the culture of unlawfulness.

“The courts have said the penalties in this area are far too low. The evidence clearly shows we need to restore a tough cop on the beat.”

The Government says the ABCC can prevent coercion and intimidation by the Construction Forestry Mining and Energy Union, against which it has a particularly powerful vendetta.

Senator Abetz said an objective view clearly shows there is “an endemic problem of industrial unlawfulness in this industry given the litany of court judgments and fines against the CFMEU for repeated and unrepentant breaches of the law”.

“It is unfortunate that the Senate did not take the opportunity today to send a strong message to the construction industry that it has to comply with the law just like everyone else and that not all senators – especially those from South Australia, Victoria, Queensland and Western Australia – chose to overlook the rampant unlawfulness in the construction industry their home states.”

Senator Abetz said the Coalition must continue to lobby crossbenchers.

“The Labor Party and the Greens continue to oppose reforms that would protect union members, workers and taxpayers.

“By their opposition they make it very clear that they care more about their relationship with militant elements of the union movement than they do about union members, workers and taxpayers.”

Australian Council of Trade Unions (ACTU) president Ged Kearney said the Government should move on.

“The ABCC is just another example of the Abbott Government's agenda to take away rights at work and deliver for the business lobby instead of supporting the millions of hardworking Australians who keep the country running,” she said.

“It's time Mr Abbott took notice of the Parliament and the community and dropped his political obsession with this bill.”