The government will introduce legislation next week to immediately abolish a tribunal that sets minimum pay rates for truck owner-drivers.

The government originally planned to delay the tribunal’s minimum pay order until January 2017 and then abolish the tribunal after the election.

On Tuesday evening the government decided to introduce legislation in the sitting week starting on 18 April to abolish the tribunal immediately. If that fails the government will settle for a bill delaying the order and abolish the tribunal after the election.

The move follows a push by the senator Glenn Lazarus, backed by Jacqui Lambie, to immediately abolish it. Lambie also called for powers to force businesses to pay independent drivers within 30 days of a completed job.

The employment minister, Michaelia Cash, said: “The government will stand shoulder to shoulder with the owner-drivers to ensure that their livelihood is not destroyed by the payment order.

“This is a test of leadership for Bill Shorten. This is an opportunity for the Labor party to fix the mess they created.”

Cash labelled the road safety remuneration tribunal part of a “sweetheart deal” with the Transport Workers Union and said its pay order would “destroy tens of thousands of family businesses across Australia” if not torn up.

On Monday Shorten reiterated Labor’s position that it was in favour of setting minimum pay rates for independent contractors, which are designed to reduce road deaths by removing financial incentives to skip breaks or speed.

While Labor resisted calls to abandon the road safety remuneration tribunal, Shorten instead offered to work with the government to delay roll out of the new minimum pay order for owner-drivers.

On Monday Lazarus initiated the call for the government to abolish the tribunal immediately.

On Tuesday Lambie said: “I support Senator Lazarus’s plan to immediately abolish the [road safety remuneration tribunal] whose pay decision would have killed off 35,000 Australian small and family trucking businesses while giving an unfair advantage to big fleet operators.”

She said the government’s original plan to abolish the tribunal after the election would have constituted “manipulating this terrible trucking crisis for political gain”.

Lambie said drivers not being paid had a big effect on safety. She called on the government to give the National Heavy Vehicle Regulator power to force businesses to pay small operators within 30 days for trucking jobs.

“That’s the simplest and easiest action the parliament can take to increase Australian road safety,” she said.

The chief executive of the National Road Transport Association, Warren Clark, said the tribunal should be abolished because it “only set pay rates for a tiny specific part of the market, the mum and dad businesses”.

In conversation with Lambie on Tuesday, Clark said abolishing the minimum rates was “super urgent”. Delaying the order until January 2017 would improve the situation of independent contractors who might lose work under new rates but Clark warned the uncertainty could still see them lose jobs.

“My way of thinking is the confidence can be brought back into the market the sooner we get rid of it,” he said.

Clark backed Lambie’s call for truck drivers to be paid in a timely manner.

“We have these larger businesses pushing out payment terms to 120 days,” he said. “Who can survive on getting their money every 120 days? When they’ve got wages, fuel bills and maintenance bills to pay, and they’ve got to be paid at the end of the month?

“One of the most crucial thing [is for big companies to] pay your bills on time, let [drivers] pay their bills on time and stop using them as your bank.”

The senators Dio Wang, Ricky Muir and John Madigan have not given support to the idea of abolishing the tribunal, instead favouring delay of its pay order.

Madigan warned while urgent action was needed to help owner-drivers, “it would be a kneejerk reaction to abolish the tribunal without proper consideration of an alternative”.

“The [tribunal] should not be kicked to the kerb without giving consideration to how these concerns will be met,” Madigan said. “There needs to be further discussion about a suitable replacement if that, in fact, is the best way forward.”