Rick Santorum would encourage one of his daughters to see a pregnancy created through rape as "a gift of human life" and urge her to not consider an abortion, the socially ultra-conservative Republican presidential candidate has explained.

In an interview with CNN's Piers Morgan show, the former Pennsylvania senator was asked at length about his hardline views on abortion, which he would seek to ban via a constitutional amendment.

Santorum said he had thought deeply on the issue: "When I decided to run for public life I was informed very quickly people wanted to know what my position on that was, so I went through the process of trying to better understand the facts. It became very clear to me that life begins at conception and persons are covered by the constitution, and because human life is the same as a person, to me it was a pretty simple deduction to make that that's what the constitution clearly intended to protect."

Asked by Morgan what he would do if one of his two daughters said they had been raped and were pregnant, and were "begging you to let her have an abortion", Santorum said: "I would do what every father would do – to try to counsel your daughter to do the right thing."

Asked whether this would rule out abortion even if the daughter felt having the child would ruin her life, he explained: "You can make the argument that if she doesn't have this baby, if she kills her child, that that too could ruin her life.

"This is not an easy choice, I understand that. As horrible as the way that daughter or son was created, it still is her child, and whether she has that child or doesn't it will always be her child, and she will always know that."

He added: "I believe and I think that the right approach is to accept this horribly created, in the sense of rape, but nevertheless, in a very broken way, a gift of human life, and accept what God is giving to you. As you know, in lots of different aspects of our life we have horrible things happening. I can't think of anything more horrible, but nevertheless we have to make the best out of a bad situation. And that is making the best of a bad situation."

Questioned on how this belief in the ultimate sanctity of human life squared with his support for the death penalty, Santorum said he would only approve executions if the accused was proven to be guilty beyond any doubt. He said: "I would say when there is certainty – and there are occasions when there is certainty – that's the case when capital punishment can be used."

Santorum's stance will once again delight his deeply religious support base, and dismay those who fear he, more even than other socially conservative candidates, seeks to fundamentally change US laws according to his staunch Catholic beliefs.

He has faced criticism during the Republican race for comments made in a 2003 interview that appeared to equate consensual homosexual acts with incest, bigamy or adultery – comments that outraged equality activists, even after Santorum said they had been misinterpreted.

Santorum narrowly won the first leg of the Republican race, the Iowa caucus, but has struggled since. At the weekend he came a distant third in the South Carolina primary, winning 17% of the vote, and is not seen as a notable threat to the frontrunners, Mitt Romney and Newt Gingrich.