Australian companies with more than 1,000 employees would have to publicly reveal how much they pay women compared with men under a federal Labor government.

But the prime minister, Scott Morrison, has said “you’d want to be confident you’re not setting up conflict in the workplace” before implementing such a policy.

Labor says the gender pay gap is “stubbornly high” and women working full-time still get paid almost 15% less than men working full-time.

“It is unacceptable this has barely changed over the last two decades,” said a joint statement from the deputy opposition leader, Tanya Plibersek, and the opposition employment spokesman, Brendan O’Connor, on Sunday.

On average, a woman working full-time earns about $27,000 per year less than a man, the statement said.

“We must do better,” it said, adding that a Labor government under Bill Shorten would “act to shine a light on the gender pay gap in Australian companies”.

Labor would also change the Fair Work Act to prohibit pay secrecy clauses and require the Workplace Gender Equality Agency to publish a list showing whether large companies had undertaken and reported a gender pay gap audit.

Companies already report their gender pay data to the Workplace Gender Equality Agency but Labor would make it public, the statement said.

“People will be able to search a gender pay equity portal to find out a company’s overall pay gap, and the pay gaps for managerial and non-managerial staff.”

All Australian government departments and agencies would also have to conduct gender pay audits within the first year of a Labor government.

The policy is an important step towards fair pay for women, says the Australian Council of Trade Unions.

Its president, Michele O’Neil, said it would ensure employers would not be able to punish their employees for discussing pay with each other.

“Working women need measures to combat the systematic society-wide undervaluation of work done by women,” she said on Sunday. “This must include moving away from reliance on the narrow and failing enterprise bargaining system.”

The prime minister, Scott Morrison, responded by stating that the gender pay gap had increased under Labor and closed to 14.5% under the Coalition government.

Under Labor, the gender pay gap increased from 15.5% to 17.2%. Under our Government it has fallen to 14.5% and heading in right direction #Moretodo. — Scott Morrison (@ScottMorrisonMP) September 22, 2018

At a press conference in Sydney, Morrison said he was “open-minded” about the proposal to increase transparency but questioned whether it would help companies achieve the goal of pay equity.

Morrison said that pay equity reporting was already in place for companies with more than 1,000 employees and it was up to companies whether to publicly announce those results “if they wish to to tell that as part of their story”.

“You’d want to be confident you’re not setting up conflict in the workplace,” he said. “I don’t want to set one set of employees against another set of employees.”