National director Bob McCoskrie said its own polling carried out by Curia Market Research showed 68 per cent of New Zealanders backed paid father leave.
"The period immediately following the birth of a child is demanding and difficult for mums, especially with sleep deprivation, recovering from childbirth, and coping with the existing demands of siblings," Mr McCoskrie said.
"This will promote hands-on parenting by fathers, which is a good thing."
At present, dads are entitled to two weeks' unpaid leave. The primary eligibility for paid parental leave lies with the mother. If her partner is also eligible then she may transfer all or part of her entitlement to her partner.
A 2009 report by the Families Commission found almost half the 1721 fathers surveyed were unable to take parental leave. After the publication of that report, the commission called for fathers to be given their own leave entitlement.
Paid maternity leave will be extended to 18 weeks next month.
The Labour bill, in the name of Sue Moroney, would extend paid parental leave to 26 weeks from April 2018. The bill is now before a select committee for public submissions.
A spokesman for Finance Minister Bill English has previously said, if the bill passed its third reading, the Government would use its financial veto to block it, as the policy was not budgeted for.
Parties that supported the first reading of the bill - the Parental Leave and Employment Protection (Six Months' Paid Leave and Work Contact Hours) Amendment Bill - were Labour, Greens, New Zealand First, Maori Party and United Future. National and Act opposed it.
It is not clear if the legislation still has the support to pass its second reading.
Paid parental leave in New Zealand began on July 1 , 2002 with 12 weeks leave.
Paid father leave
• There are calls for fathers to newborns to get at least two weeks' paid leave.
• "Father leave" was introduced in Australia in 2011, and is in place in a number of other countries including Sweden.
• At present, dads are entitled to two weeks' unpaid leave. The primary eligibility for paid parental leave lies with the mother. If her partner is also eligible then she may transfer all or part of her entitlement to her partner.
• Family First NZ has today called for paid father leave. In the past, the Families Commission has supported calls for such leave.
• Paid maternity leave will be extended to 18 weeks next month.