Urgent reforms in the child support system are needed to halt the "tragic" scale of family breakdown, Families Minister Maria Miller said.
Statistics show that one in five children from a broken home loses touch with a parent within three years and never sees them again, while many more lose contact as they grow older.
The Government will today propose the biggest overhaul of child maintenance for a decade, arguing that the current system encourages conflict between parents.
Speaking in the Daily Mail, Mrs Miller said: "We know that if effective financial arrangements are in place, those parents are much more likely to stay in contact and much more likely to have a strong relationship with their children. Staying in contact with both parents is absolutely critical to give a child the best start in life."
The minister said the latest figures showed there were 3.5 million children from broken homes, with almost half having no effective maintenance arrangements.
"Twenty per cent of children from separated families lose contact with the non-resident parent within just three years," she added.
"That is a tragedy. But the current system entrenches conflict when families separate."
Under the proposals, separating parents will be encouraged to find a settlement on their own and those who insist on State intervention will now have to pay a fee.
Payments will be overseen by the Child Maintenance and Enforcement Commission, which is taking over the work of the Child Support Agency.
Ministers claim there is currently a £4bn arrears in maintenance payments from non-resident parents.
Mrs Miller said the child maintenance system costs £460 million a year.
She also pointed to research that suggested children who are not brought up in a two-parent family are 75% more likely to fail at school, 70% more likely to become a drug addict, 40% more likely to have serious debt problems and 35% more likely to become unemployed or welfare dependent.
Ms Miller added: "We know that the most effective and enduring arrangements are ones that parents come to themselves."
Nicholas Cusworth, vice-chairman of the Family Law Bar Association, said the state-sponsored CSA model for arranging child maintenance had not worked, and that anything which encourages separating parents to agree terms between themselves would be "a thoroughly good thing".
"If more couples can be encouraged to agree levels of child maintenance between them without recourse to the Government, then that is to be welcomed," Mr Cusworth told BBC Radio 4's Today programme.
But he warned that the cost of the new system would fall upon the poorest parents who do not have assets to divide, and particularly mothers who are unable to contact the fathers of their children.
"It will hit the poor, because where a mother is unable to contact a father or where any agreement between her and the father may still leave the mother reliant on benefits, in those circumstances there will still be need for recourse to the Government scheme and in those circumstances there will be a charge," said Mr Cusworth.
"Scrapping the scheme and starting again is a thoroughly good idea. Charging everyone who uses the scheme - unless there is domestic violence - is not such a good idea."
But Mrs Miller told Today: "The new system will have not just support for people to make their own arrangements but the statutory system will be there to help people who can't come to their own arrangements.
"There will be a charge in place for them to use that, but for the poorest people in society, the upfront charge will be £20, so we are not talking about an enormous amount of money.
"This will still remain a heavily subsidised state maintenance system."
Barnardo's chief executive Martin Narey added: "Barnardo's notes the intention to encourage parents to exercise responsibility and make their own arrangements to provide financial support for children.
"That may work in the majority of cases. But the Government need to tell us what will happen to those parents who are unable to reach amicable settlement and equally unable to pay for a statutory service.
"If the welfare of the child is to remain paramount then the system must make allowances for vulnerable families whose hands are tied by the strain of living in poverty."