Biden, a Democrat, believes that abortion should be legal while Ryan opposes it except in the case of rape, incest, or if the mother's life is in danger.
Vice-President Joe Biden and Republican Paul Ryan on Thursday offered sharply different views on abortion policy although they both said their Catholic faith had shaped their personal beliefs on the thorny topic.
In a discussion that reflected the divisions seen between liberal and conservative Catholics, Biden and Ryan sparred over whether abortion should be legal and if the Supreme Court should be the deciding voice on the issue.
Less than four weeks before the November 6 election between President Barack Obama and his Republican rival Mitt Romney, the vice-presidential candidates had their only debate on a range of topics that included the hot-button issue of abortion.
The two men were asked how their Catholic faith had impacted their views on abortion. Biden, a Democrat, believes that abortion should be legal while Ryan opposes it except in the case of rape, incest, or if the mother's life is in danger.
"You want to ask why I'm pro-life? It's not simply because of my Catholic faith," said Ryan. "That's a factor of course. But it's also because of reason and science." To illustrate his view that life begins at conception, the Republican congressman from Wisconsin recounted a story of how he and his wife saw the heartbeat of their first-born child when she was just the shape of a bean on an ultrasound image. As a result, their first born daughter, Liza, was given the nickname "Bean."
"I understand this is a difficult issue and I respect people who don't agree with me on this," Ryan said. Though he has expressed more conservative views on abortion in the past, Ryan said a Romney-Ryan administration would allow abortion under certain circumstances.
Biden said he personally agrees with the Catholic Church's position on abortion, but he did not think that those personal views should be imposed on others who may have different religious beliefs.
"I just refuse to impose that on others, unlike my friend here," Biden said.
"I do not believe we have a right to tell women that they can't control their body. It's a decision between them and their doctor."
Surveys by the Pew Research Center showed that a majority of Catholic registered voters think abortion should be legal in most or all cases.
Biden said he would not interfere with the Supreme Court's landmark 1973 Roe v. Wade ruling legalising abortion - a ruling that Republicans have long fought to overturn.
He also said the next administration may appoint one or two new justices to the high court and that could impact whether Roe v Wade stands. The US Supreme Court is narrowly divided on abortion rights.
The last time the Justices took up the issue was in 2007, when by a 5-4 vote they upheld the federal Partial-Birth Abortion plan. Two of the four Justices that opposed the plan have retired during Obama's administration and been replaced by liberal Justices.
Ryan said he did not think that "unelected judges" should make a decision regarding the legality of abortion but rather that it should be made through elected representatives.
Romney has pledged to appoint Supreme Court justices who would overturn the ruling, but earlier this week the Republican presidential candidate said if he is elected he would not pursue specific legislation targeting abortion.
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