The Minister for Social and Family Affairs, Mr Brennan, is planning to replace the lone-parents allowance with a "family friendly" child benefit scheme.
Mr Brennan said many single-parent families were finding themselves in a poverty trap and would be given a better chance to enter the workplace or education system under new welfare proposals.
The new system would also end the provision where extra benefits are paid on the basis that a parent is living alone at all times.
A range of options are being studied by a high-level group of officials from a number of Government Departments that will report to the Minister in the coming months.
The Minister also rejected recent suggestions that a generous welfare system is leading to the emergence of increasing numbers of lone-parent families.
"I don't believe single parents got themselves into this situation for financial reasons. In choosing to have and rear children on their own they deserve our respect and support," he told The Irish Times.
"We should be looking at this in terms of social policy which allows single parents the chance to enter the education system or the workplace if they so wish."
Mr Brennan declined to comment directly on the controversy generated by an article by Kevin Myers in The Irish Times last week, but added that it was unfair to stigmatise children from single-parent families.
"I don't think it's fair to ascribe to any group that they are more likely to be in trouble, or whatever. I don't think that's fair.
"Any statistics in that regard should be studied, but there are a whole lot of people who come from single-parent families who have given a marvellous account of themselves," he said.
Mr Brennan expressed unease at the way the lone-parents' allowance was structured, under which inspectors were employed to ensure single parents were not living with a partner.
"I've all these inspectors going out to ensure that there's not a father living in the house - I don't think that's very good social policy. I'm interesting in getting behind the payments and ensuring people have a decent quality of life," he said.
He said statistics suggested that between 2 and 3 per cent of single parents were under the age of 20, which "debunked the myth" that teenage girls were being lured into a welfare trap.
Mr Brennan added that the average single parent was in their late 20s, and that a quarter of lone parents were either separated, divorced or widows.
Lone parent support groups, such as One Family, yesterday gave Mr Brennan's proposals a cautious welcome.
The director of One Family, Ms Karen Kiernan, said the transition from welfare to work or education for many single parents were very difficult. Parents would welcome any changes that would ease this change, along with measures such as affordable childcare and flexible working hours.
Fine Gael's social and family affairs spokesman, Mr David Stanton TD, gave the proposals a cautious welcome but said making changes to the welfare system required great care to ensure no hardship was caused.
"I am strongly in favour of any move which would facilitate parents living together in the family home for the benefit of their children," he said.
"The Minister must also be very careful around the phasing out of other benefits, such as rent allowance, as there is a danger of creating disincentives or, indeed, of replacing one poverty trap with another."