Should Mr Hunt decide to give the treatment the green light the technique could be written into law as early as next year, making Britain the first country in the world to allow human trials.
Lisa Jardine, chair of the Human Fertilisation and Embryology Authority (HFEA), which is conducting the consultation, said the issue was of "enormous public interest", and not just to affected families.
She said: "We find ourselves in unchartered territory, balancing the desire to help families have healthy children with the possible impact on the children themselves and wider society."
Comparing the ethical debate with the birth of Louise Brown, the first IVF baby, in 1978, she added that many people had expected the child to be a "monster" and seen conception outside the womb as "absolutely appalling", but that IVF has since become commonplace.
She said: "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."
An estimated one in 200 children born in Britain each year is thought to have some form of mitochondrial disease, with defects in anywhere between a handful and 90 per cent of their mitochondria.
In the vast majority of cases, where the number of defects is low, there are no symptoms and the condition is never even diagnosed.
But in about one in 6,500 people the level of damage causes the development of severe medical conditions including muscular dystrophy and ataxia, a neurological condition affecting balance, coordination and speech.
About 99.8 per cent of our DNA, including all our visible characteristics, is contained in the cell nucleus and is passed down from our father and mother in equal measure.
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'Three-parent baby' fertility technique could be made legal