The streamlined paid parental leave will combine Parental Leave Pay and Dad and Partner Pay from July 1. Paid parental leave will then increase from 18 weeks to 20 weeks.

The changes also encourage parents to share care by allowing either parent able to claim first and allowing access to the entitlement in multiple blocks with periods of work in between.

From the end of March, parents can avoid delays by pre-claiming paid parental leave up to three months before the expected date of birth or adoption.

ACT senator David Pocock, a PPL supporter, proposed that businesses with fewer than 50 workers have the option of paying the Commonwealth the leave directly or to have Services Australia pay it, pointing to small businesses being increasingly run by women who are "having to shoulder" this red tape burden.

After debating his proposal, he declined to move it as he was still negotiating with the government.

In a twist, Liberal senator Anne Ruston leapt to her feet to move Senator Pocock's red tape reduction proposal. It failed 34 votes to 29, and the Paid Parental Leave Amendment Bill passed the Senate without amendment.

The independent senator said on Monday that "so much" more needs to be done to accelerate and modernise the current tax-payer funded entitlement to "help close the participation gap and by extension, the pay gap". He also wants to increase the participation of fathers.

He also described the government bill as a "first step", noting paid parental leave is not a replacement wage, but a minimum wage payment.

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He said more needs to be done to increase the participation of fathers, citing 80 per cent of all paid parental leave being claimed by women. Senator Pocock also said it was a shame that the "use it or lose it" two weeks is not being expanded.

The Greens also failed to amend the paid parental leave changes, including to make it available for post graduate work and to add the superannuation guarantee, to reduce the super gap between men and women.

The Albanese government is expected to introduce legislation in the second half of the year to expand the scheme to 26 weeks by 2026.