The potential treatments, currently only at research stage in laboratories in Britain and the United States, would involve implanting genetically modified embryos into women for the first time.
The techniques have become known as three-parent in vitro fertilization (IVF) because the offspring would have genes from a mother, a father and from a female donor.
They are designed to help families with mitochondrial diseases - incurable inherited conditions passed down the maternal line that affect around one in 6,500 children worldwide.
"This is uncharted territory," said Lisa Jardine, chair of the Human Fertilisation and Embryology Authority (HFEA) which is running the consultation until December.
"If this is allowed...it has consequences in perpetuity."
The HFEA is Britain's independent regulator for IVF treatment and embryo research and was asked by the British government to "take the public temperature on this important and emotive issue," Jardine said.
The new potential treatments involve intervening in the fertilization process to remove faulty mitochondrial DNA, which can lead to a range of inherited conditions including fatal heart problems, liver failure, brain disorders, blindness and muscular weakness.
The techniques would effectively replace mitochondria, which act as tiny energy-generating batteries inside cells, so a baby does not inherit faults from its mother.
Britain is in the vanguard of research in this area, so ethical concerns and scientific advances here are closely watched around the world - particularly in the United States where scientists are also working on DNA swap techniques.
Jardine, whose organization will report back to government in early 2013, said she wanted to hear from people from all walks of life, all backgrounds and all levels of expertise.
Medical science of this kind, especially when it involves human reproduction, has the potential to "immediately alter the nature of society to all eternity," she said.
There is a need, she added, to balance "the desire to help families have healthy children with the possible impact on the children themselves and wider society."
"IMPORTANT AND EMOTIVE ISSUE"
The consultation on the HFEA website at www.hfea.gov.uk is open to anyone.
Among questions contributors are asked to consider are: how a child born from this sort of technique might feel?; whether the child should be told?; whether their sense of identity might be affected?; what the rights of the female donor might be?; whether the donation of mitochondrial DNA should be viewed as similar to egg or sperm donation, or more like blood or tissue donation?; and who should decide who can access the treatments?
"Every person in the UK and beyond ought to have a view, and we want to reach as many of those people as possible," Jardine told reporters at a briefing in London.
Scientists are researching several three-parent IVF techniques. One being developed at Britain's Newcastle University, known as pronuclear transfer, swaps DNA between two fertilized human eggs. Another, known as maternal spindle transfer, swaps material between the mother's egg and a donor egg before fertilization.
A British medical ethics panel that reviewed three-parent fertility treatments for mitochondrial diseases decided in June they were ethical and should go ahead as long as research shows they are likely to be safe and effective.
Some pro-life campaigners have already criticized the scientific research, saying that creating embryonic children in a lab abuses them by subjecting them to unnatural processes.
The HFEA said other critics may worry that modifying embryos to avoid disease could be the first step towards the creation of "designer babies," whose genetic makeup could be modified as embryos to ensure certain traits such as height or hair color.
Health experts, research groups and medical charities welcomed the consultation.
"This is our chance to have a thoughtful and insightful discussion about the issues, benefits and risks of these techniques and ... make an informed decision about techniques that could yield an answer for some debilitating and currently incurable diseases," said Sharmila Nebhrajani, head of Britain's Association of Medical Research Charities.