By Rosa Prince, Political Correspondent
Last Updated: 4:00PM GMT 17 Mar 2009
The requirement for compulsory registration of both the mother and father on birth certificates forms part of the Welfare Reform Bill, which MPs vote on for the final time.
Ministers say that as well as making it easier to track down those attempting to avoid paying maintenance, the scheme also provides official recognition of the importance of fathers in children's lives.
Critics accused the Government of sending out mixed messages after separate measures contained in the Human Fertilisation and Embryology Act, which come into force next month, gave women who had conceived using In vitro fertilization the right to name anyone they chose, including same-sex partners, as the second parent on birth certificates
Some charities also oppose the plans, which give men who are estranged from the mother the right to declare that they are the father of the child, saying this could put abused women at risk.
Seven per cent of babies - 45,000 a year - are registered without a father's name on their birth certificate, four out of 10 of them to teenager mothers.
When he announced the measures last year, James Purnell, the Work and Pensions Secretary, said that the Government wanted to: "support children whose parents' relationship has broken down."
He added: "We will bring forward legislation so that it becomes the default option for both parents to register the birth of their child whether they are married or not."
Under the terms of the proposed law, women would have to name the father of the child unless they could provide a valid reason for not doing so - such as being unsure of his identity.
Men who dispute paternity or refuse to acknowledge their child will be offered DNA tests.
Fathers will also be able to make a formal declaration stating that they are the parent in the event that an estranged ex-girlfriend has left them off the certificate, giving them automatic parental control unless the woman goes to court to overturn it.
Charities including the NSPCC and Gingerbread complain that this could help abusive men gain access to battered women.
Janet Allbeson, of Gingerbread said: "We are deeply concerned that the procedures for joint registration, could put women who have suffered domestic abuse, at further risk of violence or psychological abuse.
"A pregnant woman could, in theory, escape domestic violence only to find that her abuser has registered himself as the father of her child and has automatic rights to the child."