But Liberal Democrat science spokesman Dr Evan Harris has said the changes are long overdue.
The government is proposing to change the law on the issue in the wake of advice from England's Chief Medical Officer, Professor Liam Donaldson.
On Wednesday, Professor Donaldson and his advisory group called for the changes, which are likely to speed up the development of new treatments for many currently incurable illnesses, such as Parkinson's disease.
'Ethically unacceptable'
But Dr Fox told BBC Radio 4's Today programme that if forced to make the choice between therapeutic cloning with embryos or no cloning, he would vote for "none".
He said he was against using embryos as "spare parts", but was more comfortable with the use of adult cells for cloning.
"If they were adults' stem cells, we'd be taking cells from ourselves and developing them into other tissues which we can use for ourselves or for other adults.
"That is less of a problem to me. My bigger reservation is taking cells from embryo clones.
"I think the use of embryos for this sort of experimentation is not acceptable. Because I find it ethically unacceptable, I would be against it for therapeutic cloning."
Traditional free vote
It is unclear exactly when the government would put the issue before Parliament but it is likely to be before the end of the year.
Dr Harris, who is also putting forward a Private Member's Bill, said the government should act as soon as possible, as patients suffering crippling diseases were waiting for a cure.
And he said: "The Tories should not make party political attacks on the proposals which are traditionally free-vote matters."
Turning to the government's additional plans to tighten the existing ban on reproductive cloning, he said it must not be used as an excuse to put any delay on therapeutic cloning which he said was urgently needed.
He added that Professor Donaldson's report was "very pro-life" in that it could see the lives of people with cancer, Parkinson's disease and organ failure saved by more detailed research into stem cells.
Labour peer and fertility expert Lord Winston welcomed the Donaldson report. He said those who favoured the recommendations were only asking for a very "modest extension" of what was already permissible.
Underling the importance of being able to use embryonic stem cells in medical research, he highlighted the "unique potential" they had to develop into any kind of cell in the body - unlike adult stem cells whose use he said was "doubtful".
He told BBC News 24 he believed it was more ethical to transplant cloned tissue which involved no risk to a tissue donor, unlike more conventional techniques.