Almost 70% of mothers believe men are just as good at looking after children as they are, a think tank has said.
The think tank wants to see paternity leave increased
A poll of 1,000 people for the Fatherhood Institute found most women had faith in men's parenting skills, but felt men's role was undervalued.
The think tank said on average men spent one month less with their children every year than women.
It wants longer parental leave for fathers and more effort by midwives, teachers and others to engage fathers.
Of those polled, 95% felt it was important for fathers to spend time caring for their children during their first two years.
But two-thirds of women and almost three-quarters of men said society valued a child's relationship with its mother over that with its father.
Of the sample, 394 were mothers out of a total 658 parents.
The Fatherhood Institute, formerly known as Fathers Direct, said unsocial hours and inflexible working were largely to blame for men being unable to take a more active role.
Duncan Fisher, the charity's director, said: "Most mums have confidence in dads and they want them to play a bigger role.
"It is clear that parental leave and services do not meet the needs of the modern family.
"Government and policymakers need to catch up with reality because involving dads has a huge impact on a child's wellbeing and life chances."
Beverley Hughes, Minister of State for Children, Young People and Families, welcomed both the findings of the poll and the recommendations made by the Fatherhood Institute.
She said: "Fathers have told us they want to have more opportunities to share in the care of their children and to be involved by schools, children's centres and health professionals in all aspects of their child's development.
"I want to see a revolution in how teachers, midwives, doctors, early years and all children's services staff routinely talk to and provide opportunities for the involvement, not only of mothers but also fathers, from pregnancy and right through childhood and adolescence."
The think tank is calling for more to be done to ensure that fathers sign their children's birth certificates.
It wants to see an additional 25,000 fathers registered on the documents every year.