BBC News reports that Bishop Michael Evans of East Anglia said he could not agree to the new Amnesty stance and therefore resigned after the organisation vote to support the right of women to have access to abortion where pregnancy is a grave risk to their life or health.
As part of a campaign on women's rights the group is highlighting the issue of rape in society and war zones.
Bishop Evans, who wrote a special prayer for the organisation, told the BBC's Sunday programme, a move away from neutrality on abortion had caused him a problem.
"If Amnesty International becomes an organisation which affirms the right to abortion, even under certain circumstances, it is free democratically to do so.
"But it cannot expect those of us who are just as passionate about the human rights of the unborn child to feel at ease being part of such an organisation," he said.
He added: "It is this move away from neutrality that is causing the problem."
Bishop Evans is the head of the Roman Catholic Church in Cambridgeshire, Norfolk and Suffolk.
In another move, Zenit reports that Ireland's branch of Amnesty International will not promote the organization's new policy of allowing abortion in cases of rape, incest, or threats to the mother's life.
Noeleen Hartigan, director at Ireland's Amnesty International office, confirmed that the Irish branch is opting out of the controversial new policy, the Irish Times reported.
Catholic delegates attending an Amnesty International conference this week are likely to raise the issue, which has already received wide media attention.
Bishop resigns over Amnesty move (BBC News, 19/8/07)
Amnesty backs women's right to abortion (The Age, 19/8/07)
Abortion Causes Rift at Amnesty International (Zenit, 18/8/07)
Health chief tells of abortion experience (The Age, 19/8/07)
LINKS (not necessarily endorsed by Church Resources)
Amnesty International (Wikipedia)
Bishop Michael Evans (East Anglia diocese)
Amnesty refuses to budge on abortion (CathNews, 31/7/07)
US bishops pressure Amnesty over abortion (CathNews, 5/7/07)
Vatican, Amnesty in abortion stoush (CathNews, 14/6/07)
Bishops to respond to Amnesty abortion policy (CathNews, 28/5/07)