The small business minister, Bruce Billson, is trying to convince cabinet he can change competition laws to stop big business “abusing” market power, while “appeasing” the powerful Business Council of Australia (BCA) which is implacably opposed and says the move would raise prices and hurt the economy.

Cabinet is deeply divided on the issue which pits the biggest companies in the country against the small business “engine room” the government courted with its “have a go” 2015 budget.

It did not reach a decision when the competition law changes were first discussed in Adelaide on 4 August, asking Billson – who has mounted a strident public campaign for change – to come back with a presentation about the risks and benefits of the plan.

Guardian Australia has learned Billson has sent his fellow ministers a slide pack, which makes no formal recommendation, but is understood to argue that his proposed changes could “appease” the BCA and also address its claims that the competition law change would actually hinder competition and hurt consumers.

Billson has accused the BCA of peddling “nonsense” about his proposal. Ministers say the organisation and other major corporations are “pulling out all stops” to lobby against the plan.

Major companies including Telstra, Bluescope and Qantas are understood to have joined the two big supermarkets, Coles and Woolworths, as well as Wesfarmers and the BCA in a major lobbying campaign to defeat the move – which was recommended by the Harper review of competition policy.

“The big end of town has gone in really hard on this ... they are pulling out all stops,” one minister said.

But several of Billson’s cabinet colleagues – including treasurer Joe Hockey, attorney general George Brandis, trade minister Andrew Robb, finance minister Mathias Cormann and communications minister Malcolm Turnbull – are understood to have opposed the move.

The Australian Financial Review has reported that BCA leaders left a recent meeting with Tony Abbott with the understanding he backed Billson. After BCA president Catherine Livingstone spoke against the competition law changes, Abbott said “we will proceed with reforms as we see fit, even if it means changes to competition law”.

But sources said the prime minister is now keen to avoid opening another political argument or risk a campaign claiming that it is harming the economy as his government struggles to stay on message.

The agriculture minister, Barnaby Joyce, is understood to back Billson’s position.

Billson told Guardian Australia on Monday that it was “entirely unreasonable for big business to want to dictate the rules about how we make sure that big business does not harm consumers and the economy”.

“We should never lose sight of the fact that these laws are in place to put some bumper rails around the might of these businesses.”

The change – one of 56 recommendations from the Harper review – is also opposed by Labor, who Billson has accused of “drinking the BCA Kool-Aid”.

The proposed changes to section 46 of the Competition and Consumer Act would require a small business to prove that the action of a bigger business had the “effect” of substantially lessening competition, instead of being required to prove that the action had been done with that “purpose”. The change would also remove a section forbidding a big business from “taking advantage” of its market power. The BCA says this would significantly widen activities that might be caught by the act.

But the changes are vigorously supported by small business and the Australian Chamber of Commerce and Industry, independent retailers and the National Farmers’ Federation.

The say the change would encourage, rather than diminish, competition and say the claim that it would force price rises is a “furphy”. They say Billson’s proposed changes would bring Australia into line with other countries and would create a more level playing field.