A shake-up of parental leave entitlements could see fathers spend more time with their babies.
A consultation on changes to the system has been launched by Theresa May in one of her final acts as Prime Minister.
She also set out plans to support parents whose baby is born prematurely or needs an extended hospital stay.
The consultation asks questions about whether statutory paternity leave for fathers and same-sex partners should be changed.
It also calls for suggestions on ways in which the shared parental leave policy introduced in 2015 could be improved.
The consultation aims to challenge the assumption entrenched in the system that the mother must be the main carer in the early stages of a child’s life.
The Government believes that changing paternity leave could have an impact in promoting better gender equality in work and at home.
The UK is below average among leading economies in the OECD group of countries in terms of length of dedicated paternity leave offered, though it is highest on length of maternity leave, demonstrating the size of the current discrepancy.
Mrs May said: “The experience of parenting has changed almost beyond recognition over the past 40 years, with fathers wanting to share caring responsibilities more equally from the outset.
“In introducing shared parental leave, we have taken significant steps to support parents to do this, but all too often it is still mothers, not fathers, who shoulder the burden of childcare.
“It is clear that we need to do more and that’s why today we have launched a consultation calling for views on how we can improve the current system.”
Women and equalities minister Penny Mordaunt added: “Fathers should not have to rely on annual and unpaid leave if they want to be involved in the first months of their child’s life.”
Mrs May said the Government also wanted to help parents cope with the “unimaginable stress” of a premature or sick baby requiring special care.
In the UK, an estimated 100,000 babies are admitted to neonatal care every year following their birth.
For fathers and partners, that means typically their whole two weeks of paternity leave is spent with the mother and baby in hospital.
Under the new proposals, parents would receive one week of neonatal leave and pay for every week their baby is in hospital.
This would be available to mothers, fathers and partners.
Mrs May said: “Parents have more than enough on their plates without worrying about their parental leave running out and having to return to work before their precious newborn comes home.
“That’s not fair and it’s not right. So we’re also proposing a new neonatal leave and pay entitlement to make this time a bit easier for parents whose babies need to spend a prolonged period in neonatal care.”
The consultation will also consider whether firms should publish their leave, pay and flexible working policies and whether there should be a requirement to consider advertising jobs as “flexible”.
Mrs May discussed the proposals with parents during a visit to Wimbledon in south-west London.
Small business owner Philippa Harris, mother of two-year-old Toby, said she and her husband had been “very lucky” as “his organisation fully supported shared parental leave so we took three months each”.
She told the PA news agency: “I run a small business, so it was really important that I got back to work quite quickly to minimise impact.
“I took three months, he took the other three months, that allowed us to have the full six months with Toby at home.”
She said that the group of parents and Mrs May discussed the proposals for firms to be more open about their parental leave policies.
“Asking about the leave almost implies that you’re about to take six months to a year off, we really need to be much more open and flexible working is such a big thing, we felt as a group that should really enable change,” Mrs Harris said.