A group supporting one-parent families has urged the Government to use the proposed referendum on children as an opportunity to change the Constitution to give proper recognition to such family structures.
Marking International Day of Families, One Family said it wanted “equal respect and value” for single-parent families.
One in six families have just one parent and a fifth of children live in a one-parent family, the body said.
It said single-parent families are at greater risk of poverty than most other families.
Director of One Family Karen Kiernan said: "It is extremely important to recognise one-parent families for the strong family units they are and we are calling on the Government to change the Irish Constitution to reflect this.
“In Ireland, married families are given the highest respect and value in the Constitution often at the expense of lone-parents and families who can be vulnerable in areas such as poverty, skills and family supports.”
Ms Kiernan told The Irish Timesher organisation believed the proposed referendum on children's rights would be the "ideal time" to also look at family rights.
She said, however, there had been no official "appetite" for this to date.
"We believe the Constitution is out of step with the realities of family life today," she said.
In a submission to the Joint Oireachtas Committee on the Constitutional Amendment on Children last week, One Family reaffirmed its "long-term objective" to to have the definition of the family contained in Article 41 of the Constitution changed "to ensure equality for all children and their parents".
"We recognise that the climate for such a change is not there at present. We therefore recommend that the impact of the current amendment, if passed, on equality between children be closely monitored and that the government make a commitment to revisit this issue if it is found that inequalities between married and unmarried families and their children remain or increase following the referendum," it said.
One Family says the Constitution permits the State to favour families based on marriage.
It claims the proposed constitutional amendment would not prevent such discrimination from being perpetrated.
"At best, there is a real danger that this amendment will make little difference to children living in non-traditional family arrangements."
The theme for this year's International Day of Families is Fathers and Families – Responsibilities and Challenges.
According to One Family, 14 per cent of one-parent families here are headed by fathers.
UN Secretary General Ban Ki-moon said: “Recent research has affirmed the positive impact of active involvement by fathers in the development of their children.”
But he said challenges persisted for fathers, and for society and social policy.
“Too many men have difficulty assuming the responsibilities of fatherhood, often with damaging consequences,” he said.
“As our understanding of fatherhood grows, there is an opportunity for men to re-envision imaginatively what it means to be a father and to see opportunities to make a difference in communities.”