The opposition also wanted the recommendations of the banking and aged care royal commissions implemented before the government's "ensuring integrity" laws are debated.

The three lofty conditions were designed to ward off a vote on the legislation, which would make it easier to deregister unions and ban officials.

The Morrison government suffered a humiliating defeat last year when One Nation made the shock decision to shoot the bill down in the Senate in December.

But Labor frontbencher Katy Gallagher's motion was voted down 36 votes to 31 on Wednesday, with minor parties One Nation and Centre Alliance opposed.

Labor's motion would have erected a parliamentary roadblock until:

* legislation to establish a national integrity commission receives royal assent

* all recommendations from the banking royal commission are legislated

* the interim recommendations of the aged care royal commission are legislated.

Tasmanian independent Jacqui Lambie, who looms as the crucial senator on the union bill, abstained from the vote.

The government has flagged it will have another crack at trying to pass the legislation, arguing the reforms would clamp down on unions repeatedly breaking the law.

Attorney-General and Industrial Relations Minister Christian Porter is continuing to negotiate with Senator Lambie over the bill's passage.

Liberal frontbencher Jonathon Duniam said the government was responding to bullying and harassment in workplaces.

"The bill should not be delayed any further by a Labor Party desperate to continue the shameful protection racket they've run for militant law-breakers for far too long," he said.

Greens senator Mehreen Faruqi said the legislation was an attack on workers and their unions.

"There is no integrity in this bill. In fact, there is no integrity in this government either," she said.

Australian Associated Press