She said that after passing the civil partnership legislation for gay and lesbian couples, there was now an opportunity to tackle the issue of single fathers' rights.
"It's heart-breaking to meet these dads. They are well aware where their own personal relationship cannot be resuscitated but they want to be decent dads to their children," she said.
Currently, the mother is the sole guardian if a child is born outside marriage and fathers must apply to the courts for guardianship rights.
Ms White, who is the Green Party deputy leader, said one of the issues currently being considered by Law Reform Commission was whether single fathers should get automatic guardianship rights.
"We have to have to have a clear path for access -- guardianship or custody or even familial visits of separated and single dads so those visits can be facilitated and not frustrated by a partnership that has been dissolved or that has irretrievably broken down," she said.
Since being appointed as the Junior Minister for Equality and Integration last May, Ms White said she had been contacted by a number of "grieving fathers" and had visited fathers' groups such as Families, Fathers & Friends in Galway city.
"There is a well of unhappiness out there. Their stories of the family law courts in Ireland, their quest for access to their children and their despair in many cases have prompted me to consider how we deal with this painful issue," she said.
And when debating the issue on local radio in her Carlow-Kilkenny constituency, Ms White was also contacted by many grandparents who complained that they were no longer getting access to their sons' children in the wake of relationship breakdowns.
"It is a real knock-on effect and it strikes at the heart of grandparents' care and love for their children," she said.
The Law Reform Commission's report on "Legal Aspects of Family Relationships" is scheduled to be published in the autumn. Ms White said she was determined it would not become just another worthwhile report gathering dust on a shelf.
"There needs to be a level playing pitch in the family courts in Ireland. We can no longer be blind to the rights of single and separated fathers and their children," she said.
Although there was some opposition in Fianna Fail to the introduction of civil partnerships for gay and lesbian couples, Ms White said she did not anticipate similar problems with new legislation on access rights for single fathers.
"I think this cuts across party political divides. Each and every one of us primarily before being politicians, we're family people and I don't think it'll meet with huge resistance from the political side," she said.