The Social Democrats legislation would see the entitlement extended from 18 to 26 weeks
The Government says it will not oppose a Social Democrats bill, proposing extended parental leave.
However it says this should be done on a paid basis.
The bill before the Dáil would see unpaid parental leave increase from 18 to 26 weeks.
Minister of State at the Department of Justice and Equality, David Stanton, gave the Government's response.
"The Government agreed with the deputies as to the need to support families.
"It agrees with the deputies and the principal of improving family leave available to parents - it is for these reasons the Government will not oppose the deputies bill this evening.
"However, the Government believes that the focus should now be on introducing parental leave on a paid basis.
"I believe that the provision of paid leave will bring much greater benefits to parents and children at this stage, rather than the further extension of unpaid leave".
The Social Democrats’ legislation would see the six months entitlement be used at different stages of child’s upbringing, and would be available until they reach the age of eight.
The current allowance is the minimum required under EU law.
Earlier Social Democrats co-leader, Róisín Shortall, said their plan would mean parents could take the time off work that they need to care for their children.
“We believe that it will assist parents in juggling their work and child minding responsibilities,” she said.
“We know that child-care is very expensive and that needs to be tackled but we also know that parents need the kind of flexibility to spend more time with their children at particular stages in their child’s life.
“In the early years especially; but also then when their children are at primary school.”
She said Ireland’s laws governing entitlement to parental leave are “very poor” by international standards, adding that the new bill acknowledges the high levels of stress facing many parents.
During his campaign for the Fine Gael leadership, Taoiseach Leo Varadkar pledged to support families by "extending parental leave, making childcare more affordable and making free education for children more of a reality."
If passed, the bill would entitle parents who have already used up their maximum allowed amount to take an extra eight weeks – provided they still have a qualifying child.
The Social Democrats have proposed extensions to paid parental leave in their alternative budget proposals for the last three years.
Additional reporting: Jack Quann and Tom Swift