Dealing with problem families is not a question of "marriage versus lone parents", Tony Blair has said.
Mr Blair said marriage was not the answer to some families' problems
The prime minister said marriage was "a good thing", but he said problems were not limited to single parent families.
He said specific intervention was needed to target dysfunctional families whose "kids have gone off the rails".
Tory leader David Cameron agreed that marriage was not the "whole answer" but said it should be supported through the tax system to recognise its benefits.
He has said that absent fathers and a lack of role models was fuelling gang culture, following the deaths of three teenagers in south London.
At his monthly press conference Mr Blair said, when it came to the most dysfunctional families who were "shut out" of mainstream society, specific intervention was needed at an early stage.
"In my view, the debate is not about marriage versus lone parents. The debate is about how you target measures specifically on those families some of whom will be lone parents - but some of whom will be couples."
He said it was important to support lone parents who wanted to get back into work and said Labour policies such as Sure Start and tax credits had benefited all types of families.
"Of course it is the case it is better to have kids in a stable relationship. Of course marriage is a good thing," he said.
But he added that with the most dysfunctional families, their problems went "far, far deeper" and required "tough measures with support at a very early stage".
The Tories support tax breaks to help families stay together.
But in a speech later on Tuesday, Education Secretary Alan Johnson will say: "Our family policy must be bias free... it's not who or what the parents are, it's what they do," he will tell a Relate conference.
"Taxation and law doesn't create strong families, it's love and compassion," he is expected to add during the speech.
He will say that the Married Couples Allowance had unfairly discriminated against four million children whose parents were not married.
Mr Cameron told the BBC that marriage should be supported.
"If you support marriage, including through the tax system, that's not insulting very hard working single mums who are doing a brilliant job bringing up their children," he said.
"It's just saying that as a society we should recognise that marriage does have benefits - that couples coming together and staying together is good for kids and good for our society. Why not say it?"
He agreed that supporting marriage was not "the whole answer", saying: "There's a huge cultural change that needs to take place. Government only plays a part, but at the moment it isn't playing its part at all."
The charities One Parent Families and NCH both said support for families did not have to mean promoting marriage or stigmatising single parents.
For the Lib Dems, David Laws said it made sense to remove barriers to people marrying and living together - including those on benefit.
He added: "Lone parenthood and teenage pregnancy are frequently accompanied by poor skills and poor aspirations.
"The government must tackle poverty amongst deprived communities in order to prevent youngsters seeing early parenthood as an attractive alternative to dead end jobs. "