Burke expressed his views in an essay that appeared in Periodica De Re Canonica, published by the Pontifical Gregorian University in Rome.
The Catholic leader says parish priests should ensure that everyone takes communion in a worthy manner, with no one taking it if they have publicly stood against the pro-life beliefs of the Catholic Church.
The essay is also meant as a response to the document the U.S. Conference of Catholic Bishops adopted in June 2004 that addresses pro-abortion politicians and communion as well as colleges giving a platform to pro-abortion commencement speakers.
"Such decisions rest with the individual bishop in accord with the established canonical and pastoral principles," the bishops said about communion. "Bishops can legitimately make different judgments on the most prudent course of pastoral action."
But Archbishop Burke said in the essay that he disagreed with the bishops deferring communion decisions to local Church officials and said a uniform policy is needed nationwide.
"The question regarding the objective state of Catholic politicians who knowingly and willingly hold opinions contrary to the natural moral law would hardly seem to change from place to place," Burke said.
He said the bishops put too much emphasis on a Canon Law saying that Catholics should do considerable self-examination to determine if their heart is prepared to receive communion.
Yesterday, LifeNews.com reported how Burke told the St. Louis Post-Dispatch he would deny communion to Giuliani.
"If the question is about a Catholic who is publicly espousing positions contrary to the moral law, and I know that person knows it, yes I would [deny communion]," Burke told the newspaper.
He said anyone who administers Catholic communion can't knowingly give it to Catholic politicians who flout the Church's teachings on abortion.
"It is a cause of concern for me and for all bishops to find ourselves in this situation," Burke told the Post-Dispatch.
The former New York City mayor was in New Hampshire campaigning and he avoided answering the comments directly, according to an AP report.
"Archbishops have a right to their opinion, you know," Giuliani said. "There's freedom of religion in this country. There's no established religion, and archbishops have a right to their opinion. Everybody has a right to their opinion."