Egan says he had "an understanding" with Giuliani that he is not to receive the Eucharist. The Catholic Church teaches "that abortion is a grave offense against the will of God," Egan said.
The cardinal said Monday that Giuliani broke that understanding when he received the Eucharist during Pope Benedict XVI's visit earlier this month. He received Communion during the April 19 service from one of the many clergymen who offered the sacrament.
Egan says he will be seeking a meeting with Giuliani "to insist that he abide by our understanding."
Giuliani's spokeswoman, Sunny Mindel, said Monday that he is willing to meet with the cardinal but added that his faith "is a deeply personal matter and should remain confidential."
Egan's statement does not address the fact that Giuliani is on his third marriage. Catholics who divorce and remarry without getting an annulment from the church cannot receive Communion.
A spokesman for Egan said that the cardinal referred to the abortion issue rather than to Giuliani's marital history because the agreement that Giuliani would not receive Communion pre-dated his divorce from his second wife, Donna Hanover.
Giuliani's first marriage was annulled based on the fact that he and his wife were second cousins once removed. Giuliani married Hanover in 1984 and they divorced in 2002, while he was New York's mayor. He has been married to the former Judith Nathan since 2003.
Communion and abortion rights became a storyline in 2004, when Democratic presidential nominee John Kerry, a Catholic, came under scrutiny for supporting abortion rights in conflict with church teaching.
Egan's criticism of Giuliani, however, is a rare case of a Catholic bishop criticizing a public figure by name. Most bishops who spoke about Communion and the responsibility of Catholic politicians did so in general terms without naming names.
Kerry's own archbishop, Sean O'Malley of Boston, endorsed the principle without naming the senator.