Labor has left the door open to pegging the minimum wage to median earnings, which one labour market expert said could result in increases of $80 a week for low-paid workers.

The shadow employment minister, Brendan O’Connor, told Sky News on Wednesday that legislating the minimum wage be pegged to a certain proportion of the median wage was one option Labor was “looking at”, but that the party would fully spell out how to fix wages before the election.

On Tuesday in a speech laying out Labor’s agenda for 2018 Bill Shorten called for a “real living wage” and noting that the minimum wage has been going “backwards relative to median wages for years”.

Tim Lyons, who ran the minimum wage case for the Australian Council of Trade Unions for seven years, seized on the comments telling Guardian Australia it signalled a “much more aggressive approach to raising the minimum wage from a future Labor government”.

United Voice and the ACTU have called for the minimum wage to be raised to 60% of the median wage, up from 54%, to provide a “living wage” to workers currently earning $36,000 a year.

Asked if it would adopt the ACTU approach, O’Connor said Labor had not set a particular target but would make another submission to the Fair Work Commission in the national minimum wage case to call for a reversal of stagnating wage growth.

O’Connor said that unemployment was falling and profits were doing “very well” but there is “no commensurate increase in wage growth”.

“That’s a concern for Labor, and that’s why Bill was declaring our intention to do something about it.”

Asked if Labor would legislate to mandate that the minimum wage should be a proportion of the median wage, O’Connor replied that was “certainly one option” and – again – asked about pegging the minimum wage he replied it was “looking at that as an option”.

O’Connor added that Labor was “mindful of the vagaries of the economy” and did not want an increase to have adverse consequences such as causing inflationary pressures.

The comments suggest Labor is considering a “soft target” for the Fair Work Commission (FWC) to aim at but to give it the flexibility not to grant any outsized increases rather than a “hard target” with no independent decision-making.

The chief executive of the Australian Industry Group, Innes Willox, said the FWC needed to set the minimum wage based on factors in the Fair Work Act including the needs of low-paid workers and “impacts on employment, inflation and business competitiveness”.

“Legislating to take away the role of the FWC in deciding what is a fair and sustainable minimum wage increase … and dictating that it must be at least 60% of median wages makes a mockery of the idea of having an independent umpire.

“The idea is a recipe for inflicting harm on businesses, damage to the economy and reduced employment prospects for low paid workers.”

In comments to the Australian Financial Review, the small business ombudsman and former Liberal politician, Kate Carnell, said Shorten’s proposal was “a war on small business” and could amount to a “devastating blow”.

“The greatest impact would be on businesses that use awards, and that is small-to-medium businesses, which make up more than 97% of businesses in Australia,” she said.

“Nearly half of our small business owners already earn less than the minimum wage and for these people, an increase in awards will mean job losses, limited employment opportunities and businesses closing.”

O’Connor also suggested public companies should provide more information about gender pay outcomes because “accountability is required about the way they treat female workers”.

He said he thought Labor could require them to publish aggregate pay outcomes for men and women because greater transparency would lead to more sensitivity about the need for equal outcomes.