The Council of Trade Unions (CTU) is calling on Parliament to ditch the rule that requires workers to be employed for six months before they can get sick leave.
A bill to double employees' sick leave entitlements from five days to 10 is before a select committee.
The CTU presented on the topic to the Education and Workforce committee during the week.
Its secretary, Melissa Ansell-Bridges, said people need to be able to access sick leave, no matter how long they have been working in the role.
She said the bill shows the doubled sick leave would not be mandatory for businesses for another two years.
Ansell-Bridges said more urgency is needed and that recent opinion polls show the public supports this.
More than 1200 people responded to an online poll by the CTU from 3-6 January this year about the impact of Covid-19 on people's working life.
Overwhelmingly, 94 percent of people supported the government's planned increase in sick leave from five to 10 days.