Two employer groups have launched an appeal to a decision that allowed a merger of the leftwing Construction, Forestry, Mining and Energy Union and the maritime and textile unions.

Meanwhile, the workplace relations minister, Craig Laundy, has renewed lobbying the crossbench over a bill to add a “public interest” test to union mergers and refused to rule out applying it to the new merger.

The Fair Work Commission decision on Tuesday to allow the new “super-union” set off a round of political recriminations directed at the Coalition, and the former employment minister Michaelia Cash, for failing to introduce the public interest test in time.

On Thursday the Australian Mines and Metals Association (Amma) and Master Builders Australia lodged an urgent appeal, which would go to a full bench of the commission, and asked for a stay on the decision allowing the merger.

Amma has briefed the government that the merger is not effective until 27 March, creating a window to pass the fair work (ensuring integrity) bill with an amendment that would apply the “public interest” test to the merger, if passed in the next two weeks.

The new super-union has caused consternation among employers and conservatives because of the CFMEU and Maritime Union of Australia’s militancy and the potential for the one union to represent workers throughout the supply chain.

Laundy told Guardian Australia: “The ensuring integrity bill remains a priority for the government but, because of Labor’s opposition, we need the support of the crossbench.”

Laundy defended the government’s handling of the bill, arguing it had not put it up for a vote in the Senate because it “simply didn’t have the numbers to pass the bill”.

“I am reaching out to the crossbench to see if that has changed,” he said. “But at the end of the day, Labor should also come to the table and support a public interest test – a test they removed from the system in 2009.”

The government will have a tough task passing the bill. With Labor and the Greens opposed, it needs nine out of 11 crossbench votes to pass.

Senator Derryn Hinch told Guardian Australia: “I believe if unions want to merge it’s up to the members to decide.”

Senator David Leyonhjelm said he would likely support the bill, with amendments, but negotiations with the government had only just begun when the commission approved the super-union.

The Nick Xenophon Team has not taken a party position on the bill, although senator Stirling Griff and One Nation’s Brian Burston have expressed concern that unions could abuse their power.

On Thursday the Australian Council of Trade Union’s secretary, Sally McManus, said the opposition to the merger was “crazy”, arguing it won’t make “a hell of a lot of difference” because unions are already able to cooperate.

She said the unions were amalgamating to “share resources – so they can make sure they have better efficiencies ... because it makes sense so they can provide better services to their members”.

Amma workplace relations director Amanda Mansini said “there is a pathway for the government to act in the national interest ... but the window is closing very fast”.

“They’ve had nearly two years to act in the national interest and now they’ve got two weeks,” she said. “This is not just about the resources and energy industry. It’s a community issue. Union militancy will affect the community’s access to household goods, medical supplies and all trade coming through the ports.”

On Tuesday the national secretary of the CFMEU, Michael O’Connor, promised the new union would “hit the ground running”.

“We are absolutely committed to a change of government, to changing the rules to restore balance and fairness into our communities and to growing our movement,” he said.

The textile union’s national secretary, Michele O’Neil, said it had a proud history fighting for “some of Australia’s lowest paid and most exploited workers”.

“The combined strength of the CFMEU, MUA and TCFUA in our new union will write a new chapter in Australia’s union movement. Ordinary workers now have a powerful new force for change on their side.”