However, a father would have to go along with the child's mother to record his details on a child's birth certificate.
Now, under the Children Act, unmarried fathers can get full paternal rights only by making a formal agreement with the mother, or through the courts.
The department yesterday announced a three-month consultation period in which it will look at comments on whether it should be made easier for unmarried fathers to acquire parental responsibility - and therefore a number of rights - subject to a number of safeguards.
A consultation paper says that automatic rights could be given to certain categories of fathers, such as those who go to register the birth with the mother.
This could be of benefit to partners who have simply chosen not to marry, or parents who want to take joint responsibility for their child, but do not wish to continue their own relationship.
Any changes making it easier for some fathers to have more access to their children would contain safeguards to protect families where the woman has been raped or otherwise victimised.
The move was welcomed by the pressure group Families Need Fathers. The chairman, Jim Parton, said: "This consultation paper is long overdue. There are too many cases caught up in litigation at the moment.
"Automatic parental responsibility would be a very good thing. It would also make child support payments less resented by those fathers who have to pay but have to fight for parental responsibility."Reuse content