Cathy Warwick, chief executive of the organisation, said the fact that maternity services are traditionally based in hospitals can make it difficult to engage fathers and educate them about the beneficial impact they can have on their child's development.
Speaking at a fringe meeting on the issue at the Labour Party Conference in Manchester, Warwick said: "I think we need to change the whole system."
"Maternity services are often the first service where men can be drawn in or turned off. They are largely delivered in large acute hospitals and that needs to change.
"We need to get them out into communities and change them into user-facing, user-led services – a complete reversal of how we are currently delivering maternity services.
"That would ensure we get to know families and people get the engagement that is needed."
Delegates heard that recent research has found that children benefit socially, economically, and emotionally as a result of engaging positively with their fathers from an early age.
Shane Ryan, chief executive of Working with Men, said latest Office for National Statistics figures show that the number of “stay at home dads” – who are primary care givers for their children – has risen to nearly 250,000.
"There is change in the air," he said.
"It gives us the opportunity to create a sensitive and thoughtful future that young people can buy into as well.
"When you look at services for engaging fathers there are very few at the moment."
He added that fathers are not used to going into settings like children's centres.
"It leads to dads being a bit unsure and lacking confidence in engaging with those services," he said.
"Practitioners are quite tentative about working with dads."
Katie O'Donovan, head of campaigns at Mumsnet, said the level of statutory paternity pay must be reconsidered if more fathers are to be encouraged to play a bigger role in their children's lives.
She said that since additional paternity leave was introduced by the coalition government, out of 285,000 fathers who were eligible, only around 1,600 took up the opportunity – just 0.6 per cent of the total.
"It will be a challenge to increase that if statutory maternity pay remains at £138 a week," she said.
"We have got to encourage fathers to know their rights, but we have also got to encourage companies to offer more than the statutory paternity pay."