"Rudy's public proclamations on abortion are pathetic and confusing. Even worse, they're hypocritical," Thomas J. Tobin, the bishop of Providence, R.I., wrote last week in a column in the Rhode Island Catholic.
Giuliani has stressed that while he's personally opposed to abortion, he believes women should be able to decide for themselves whether to terminate a pregnancy.
Tobin, who says he is not a Republican and tries to avoid partisan politics, said he would never back a candidate who supports legalized abortion, and he questioned Giuliani's integrity.
"As Catholics, we are called, indeed required, to be pro-life, to cherish and protect human life as a precious gift of God from the moment of conception until the time of natural death," Tobin wrote. "As a leader, as a public official, Rudy Giuliani has a special obligation in that regard."
The former New York City mayor's campaign declined to comment.
In 2004, Archbishop Raymond Burke caused a stir when said he would deny Communion to Democratic presidential nominee John Kerry, a Catholic who supports abortion rights. Burke later clarified the statement to say Catholics can vote for such candidates if they believe the candidate's stance on other moral issues outweighs the abortion-rights stance.