Gordon Brown has called on MPs to back stem cell research using human-animal embryos in a Commons vote on Monday.
The prime minister, writing in the Observer, said such work was a "moral endeavour" and had the potential to save and improve "millions of lives".
But Mr Brown said he respected those MPs opposed to the Human Fertilisation and Embryology Bill, which will update embryology laws, for religious reasons.
He is allowing Labour MPs a free vote on controversial parts of the bill.
In his newspaper article, Mr Brown said Britons should not "turn our back" on vital scientific advances that could speed up treatment for cancer and conditions such as Parkinson's and Alzheimer's disease.
Mr Brown's youngest son Fraser - who will be two in July - has cystic fibrosis, a life-threatening inherited disease which disrupts the way the digestive and respiratory systems work.
If we want to sustain stem cell research and bring new cures and treatments to millions of people, I believe admixed [hybrid] embryos are necessary
"The scientists I speak to are committed to what they see as an inherently moral endeavour, that can save and improve the lives of thousands and over time, millions," he said.
Labour MPs have been given free votes on three proposals in the bill, which will be debated and voted on over two days in the House of Commons.
These are the creation of hybrid embryos, "saviour siblings" - creating a child with a tissue match to save a sick brother or sister - and giving lesbian couples equal rights to IVF treatment.
In addition, they will have a free vote on amendments reducing the upper limit for abortions from 24 weeks to 22 or even 20 weeks.
The prime minister offered the free-vote deal after warnings that some Catholic Labour MPs and cabinet ministers were ready to rebel.
Mr Brown said he had "deep respect" for those who did not agree with some of the provisions in the bill because of religious conviction, but he believed Britain owed it to future generations to introduce the measures.
He went on to say that permitting human-animal "admixed" embryos to be created could help solve the current problem of the lack of human eggs from which to generate embryos.
Stem cells can be harvested from such embryos and used to create brain, skin, heart and other tissue for treating diseases.
Dawn Primarolo discusses the abortion time limit and stem cell research
"Let me be clear: if we want to sustain stem cell research and bring new cures and treatments to millions of people, I believe admixed embryos are necessary," Mr Brown said.
"The question for me is not whether they should exist, but how their use should be controlled."
Scientists at Newcastle University announced last month they had created the first part-human, part-animal hybrid embryos in the UK. The research was approved by the UK's fertility regulator, the Human Fertilisation and Embryology Authority.
Critics from the Roman Catholic Church argue the creation of such hybrids is immoral.
Meanwhile, Dawn Primarolo, the public health minister, has accused Conservative backbenchers of attempting to remove women's rights to abortion by tabling amendments to the same bill.
Mr Brown says he sympathises with those who have religious concerns
She told BBC One's Andrew Marr Show that she would be voting for the 24 week abortion limit to stay - saying there was no evidence that survival rates amongst babies born below 24 weeks had increased.
But she said she could not predict how Tuesday evening's vote on abortion would go.
She earlier told the Sunday Telegraph those wanting a cut "want to prevent it (abortion) entirely and they see that gradually changing the time limit down is the way to do it".
But Nadine Dorries, the mid-Bedfordshire MP leading the campaign to reduce the abortion time limit to 20 weeks, told the newspaper ministers had hoped the embryology bill would offer Labour MPs a chance to liberalise abortion further, but that the plan had backfired.
"They don't like it because it has not gone their way," she said.
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