Women on maternity leave or juggling several low-paid jobs would be paid superannuation under a $400m Labor plan to close the retirement gender gap.

The opposition deputy leader, Tanya Plibersek, unveiled the policy on Wednesday, saying too many Australian women retire in poverty.

Women retire on average with $113,000 less in their super than men, a gulf of 40%.

The reasons for the disparity include women taking time out of the workforce for caring responsibilities and to raise children, the gender pay gap, and the fact women are overly represented in lower paid sectors.

The disparity in superannuation outcomes for women means older single women are more dependent than men on the age pension and are the fastest growing cohort of homeless people in Australia.

Labor has pledged to phase out the $450 per month minimum income threshold for eligibility for the superannuation guarantee from 1 July 2020, with the threshold to be reduced to zero from 1 July 2024, helping people in part-time and casual work.

Around 60,000 people are estimated to become eligible for the superannuation guarantee from their employers in 2020-21 as a result of the policy, increasing to 400,000 people in 2024-25.

Labor has also pledged to pay superannuation on parental, paternal and partner leave. It will also make it easier for employers to make extra payments into a woman’s superannuation fund.

It will amend the Sex Discrimination Act 1984 to ensure that businesses are able to make higher superannuation payments for female employees when they wish to do so.

It will ask the Australian Human Rights Commission to advise on the most appropriate legislative approach and to update guidelines and advice for any organisation contemplating providing additional superannuation payments for women.

The measures to pay the super guarantee on paid parental leave and dad and partner payments and phasing out the $450 super guarantee threshold have been costed by the independent Parliamentary Budget Office to have a budget cost of $409.2m over the next four years.

Plibersek said more and more people – particularly women – were working low-paid jobs to make ends meet.

“So many more people are working two or three or four casual part-time jobs,” she said.

“We think you should get your superannuation on those smaller pay packets as well.”

Hesta has welcomed the announcement, agreeing the range of policy measures are aimed at tackling the persisting super gender gap that sees women retire with more than 40% less super than men.

“This is a comprehensive package of measures to address the gender super gap and it’s pleasing to see reforms we’ve long supported taken up such as phasing out the antiquated $450 minimum monthly super threshold and considering the impact of future super changes on women,” the Hesta chief executive, Debby Blakey, said.

Australian Associated Press contributed to this report