Members of the public are being asked how they feel over the creation of IVF babies with three genetic parents.
What they say could pave the way to a landmark change in the law that would affect future generations.
The "uncharted territory" techniques are aimed at preventing a special category of diseases caused by inherited genes.
The technique uses DNA from three people to create a baby
They involve children being conceived with the help of a third genetic "parent": a woman whose donated egg provides a source of replacement healthy DNA. A baby created this way would have a full compliment of nuclear DNA from its mother and father, plus a tiny amount of donated mitochondrial DNA.
Mitochondrial DNA is DNA taken from the mitochondria, which is the part of the cell where respiration and energy production occur.
They act as powerhouses, supplying energy and have their own set of genes, separate from those in the cell nucleus, which are only passed on by mothers.
Defects in mitochondrial DNA give rise to a range of serious and potentially life-threatening diseases including a form of muscular dystrophy and conditions leading to the loss of hearing and vision, heart problems and intestinal disorders.
The new mitochondrial replacement treatments would remove the damaged DNA, thereby breaking the generational chain of disease. But they are banned because any tampering with inherited genetic material in clinics is illegal.
A window has deliberately been left in the Human Fertilisation and Embryology Act, allowing this blanket rule to be changed by Parliament in certain circumstances. But first ministers must be satisfied that the techniques are ethically acceptable to the public.
Regulators have now launched a large-scale public consultation exercise aimed at canvassing the opinions of ordinary people rather than experts. It runs until December 7, with a report being submitted to the government next spring.
A change in the law voted in by Parliament could quickly follow. But it is unlikely that this would see the immediate introduction of mitochondrial replacement.
The final say on whether treatments can go ahead will lie with the Human Fertilisation and Embryology Authority (HFEA) which regulates IVF clinics and fertility research.
Professor Lisa Jardine, who chairs the authority, said: "The government has asked us to take the public temperature of this important and emotive issue.
"The decision about whether mitochondria replacement should be made available to treat patients is not only an issue of great importance to families affected by these terrible diseases, but is also one of enormous public interest.
"We find ourselves in uncharted territory, balancing the desire to help families have healthy children with the possible impact on the children themselves and wider society."
She recalled public attitudes to the birth of the first IVF baby, Louise Brown, in 1978.
"A lot of people thought she was going to be a monster, and the idea of what would happen if you allowed conception outside the womb was seen as absolutely appalling. Those uncharted waters are now charted waters. We've moved from uncharted territory to routine."
Speaking at a news briefing in London, Prof Jardine added: "Here, we are going that mile further which is a genetic modification of the egg. That is uncharted territory. I feel very strongly that once we have genetic modification we have to be damn sure that we are happy. Because this is not about us. This is not about our children. It's not even about our grandchildren. It's about many generations down the line what the consequences might be."
Critics fear that allowing mitochondrial DNA to be altered could be the start of a slippery slope leading to a "brave new world" of genetically modified designer babies.
Two main mitochondrial replacement techniques have been explored by scientists, pro-nuclear transfer (PNT) and maternal spindle transfer (MST).
In PNT, an early "pronucleus" containing parental DNA is removed from a fertilised egg which has not yet had a chance to develop into a multi-cell embryo. This is transferred to a fertilised donor egg whose own pronucleus has been removed and which contains healthy mitochondria.
The donor egg grows into an embryo and baby-possessing nuclear DNA from its mother and father, and mitochondrial DNA from the donor.
MST has a similar outcome but occurs before fertilisation. A spindle-shaped structure containing a mother's nuclear DNA is first removed from one of her eggs. This is transplanted to a donor egg which has had its own spindle removed, and is then fertilised by the intended father's sperm.
Once again the resulting embryo has DNA from two sources, one being the healthy mitochondria in the donor egg.
One in 200 children born each year in the UK have some form of mitochondrial disease. Not all suffer serious symptoms and not all the girls among them will pass the condition to their offspring.
It is estimated that each year only around 10 to 20 badly affected women might qualify for IVF treatment that includes mitochondrial replacement. But their treatment could prevent countless future generations from suffering mitochondrial diseases.
Last year scientists consulted about the techniques said there is no evidence to suggest that they are unsafe, but called for more research.
A new mitochondrial research centre has now been set up in Newcastle, funded by the Wellcome Trust charity.
People are being invited to air their views on the HFEA's website, www.hfea.gov.uk.
Two public events are also planned in London and Manchester. A public opinion survey will also be organised.
Prof Jardine said mitochondrial replacement raises a plethora of difficult questions such as when a child should be told that three people were involved in his or her conception.
Another tricky issue is the status of the egg donor and whether a child should have the legal right to know her identity.