The government has a role to play in promoting strong families, David Cameron has argued in a speech.
"Troubled" families should not be abandoned and people should not "shy away" from discussing the family's contribution to society, he said.
Parents with bad relationships were more likely to have a child in poverty, failing at school and ending up in prison or out of work, he argued.
Labour said it was an empty gesture given the scale of welfare cuts.
Students demonstrated outside the venue in Leeds where Mr Cameron spoke.
The coalition continues to be the focus of protests after MPs agreed to raise the level of tuition fees in England to a maximum of £9,000.
Speaking to the family guidance charity Relate, Mr Cameron said that no family should be beyond help and he made a commitment to offer "practical and modern" support to families facing "multiple pressures" such as worklessness, alcohol and drug problems.
While Labour's legacy in supporting children - through the Sure Start network of centres - was welcome, he said the last government had "shied away from saying anything meaningful about the family as a whole", particularly the relationship between parents.
"Politicians talking about families are often met by a couple of reactions: disapproval and defeatism," he said.
"Disapproval because some people say that government should concentrate on more important matters - that in public policy terms, family matters are a bit fluffy and ephemeral. Defeatism because some say that however important families are, there's little that government can practically do to help.
"I think both are wrong."
He said he was not singling out one type of relationship over another and was aware of the limits of government action.
A strong family was "defined not by its shape but by the love and support that's in it - and we need to be there for all of them", he said.
He announced that Emma Harrison - the head of welfare-to-work training company A4e - was to lead a pilot scheme to help about 500 families under particular strain by providing a system of regular, personalised support. She is also take on the role of "family champion".
Separately, the Department for Education announced an increase in funding for relationship support and counselling.
It plans to spend £30m over the next four years - a £10m increase on the existing budget - to try to improve support for couples in distress. It aims to encourage them to take up preventative support and try to make it easier for children, when relationships come to an end.
The extra funding will be found in changes to family-related local government budgets.
During this year's election campaign, Mr Cameron said he wanted to recognise marriage in the tax system.
But specific proposals for a tax break for married couples - criticised at the time by the Liberal Democrats and Labour - were dropped.
However, Mr Cameron said on Friday he still wanted to "recognise and value the commitment that people make to each other".
Labour said families with children would be more than £6bn worse off by 2014-5 as a result of coalition measures such as limiting tax credits and removing child benefit from higher-rate taxpayers from 2013.
"David Cameron is simply giving with one hand while George Osborne takes a lot more with the other," Shadow Work and Pension Secretary Douglas Alexander said.
"Of course families and relationships are vital, which is why we think they should be supported instead of facing billion of pounds of cuts to tax credits and child benefit."
And one pressure group said government welfare reforms were "working against" strong families.
"Welfare caps will hurt large families, housing benefit cuts will damage family stability and slashing working tax credits and childcare support for families in work will push families into poverty," Family Action said.
"In our experience families are best helped back to work when they get support with establishing the foundations of family life. For a lot of the vulnerable families we work with that support needs to start in the home."