Abortion is restricted in Latin America's biggest country to cases of rape, where the fetus has no brain, or where the mother's life is in danger.
The UN human rights office has called on countries where the Zika virus is thought to be linked to a rash of microcephaly cases to relax laws and allow pregnant women with Zika to terminate.
But Auxiliary Bishop Leonardo Ulrich Steiner, secretary general of the Brazilian Bishops' Conference, rejected the argument.
"Abortion leads to eugenics, the practice of selecting perfect people," he said.
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Brazil has registered 404 confirmed cases of microcephaly, where the baby is born with an abnormally small head and brain, since October last year. Another 3,670 cases are not yet confirmed.
Scientists say that the Zika virus, carried by mosquitoes, appears to cause the condition in fetuses born to mothers who have been infected.
In Brazil, a group of activists is petitioning the Supreme Court for a change in the country's restrictive abortion laws.
"Less quality of life doesn't mean less right to live," he said in the capital.
An estimated million illegal abortions are carried out each year in Brazil.