Geraldine A. Ferraro, the Democratic vice-presidential nominee, said today that she had "never made a public statement describing or misrepresenting the teachings of my church" on the subject of abortion, contrary to assertions made over the weekend by Archbishop John J. O'Connor of New York.

Ferraro, a Roman Catholic, said in a statement released here that she asked O'Connor during a 30-minute long-distance telephone call today why he had accused her of distorting the church's rigid opposition to abortion.

"He told me he was referring to a cover letter, signed by me, which was attached to material provided by a group called Catholics for Choice and which was sent to approximately 50 members of Congress in 1982," Rep. Ferraro (D-N.Y.) said in the statement. "I pointed out to the archbishop that I have never made a public statement describing or misrepresenting the teachings of my church."

The letter, released in Washington today, invited some of Ferraro's Catholic colleagues in the House to a briefing by a Catholic group that favors freedom of choice on abortion. In the letter, Ferraro wrote that the briefing would show that "the Catholic position on abortion is not monolithic and there can be a range of personal and political responses to the issue."

In what has become the latest incident in the persistent campaign issue of religion and politics, Ferraro also said she told the archbishop that "my foremost duty as a public official is to uphold the United States Constitution, which guarantees freedom of religion. I cannot fulfill that duty if I seek to impose my own religion on other American citizens."

Her rebuttal follows two days of pointed criticism from O'Connor. In brief remarks after celebrating mass on Sunday, the archbishop said Ferraro had erroneously suggested that Catholic doctrine was "open to interpretation" regarding abortion.

On Saturday night, before speaking to the Pennsylvania Pro-Life Federation, the archibishop also criticized Ferraro, by name for the first time, as having "said some things about abortion relative to Catholic teaching which are not true."

"There is no variance, there is no flexibility, there is no leeway as far as the Catholic Church says," the archbishop added Saturday. "I have absolutely nothing against Geraldine Ferraro; I will not tell anybody in the United States you should vote for or against Geraldine Ferraro or anybody else."

O'Connor also said that Ferraro "doesn't have a problem with me" but rather "if she has a problem," it is with Pope John Paul II. The archbishop quoted the pope as saying, "It is the task of the church to reaffirm that abortion is death. It is the killing of an innocent creature."

On neither occasion did O'Connor offer specific examples of how Ferraro had distorted Catholic doctrine on the subject.

Ferraro's strategists believe it is ironic that not since John F. Kennedy in 1960 has the religion of a candidate for national office been as sensitive an issue as it is in this election -- but with the twist that Kennedy was criticized by some non-Catholics as being a tool of the Vatican while Ferraro is under fire from the church for her alleged distortion of church doctrine.

Kennedy largely deflated suspicion of his Catholicism by delivering a celebrated speech in Houston 24 years ago this week in which he vowed, if elected, to fulfill his duties under the Constitution. Ferraro's aides are hoping for a similar breakthrough. She is likely to meet with O'Connor Friday night when both are scheduled to attend a dinner in New York, according to press secretary Francis O'Brien.

The issue is particularly nettlesome for Ferraro because it distracts from her campaign agenda and threatens to cloud two of the ethnic characteristics that helped her broaden the Democratic ticket: her Catholicism and her Italian heritage.

Ferraro's oft-stated position on abortion is that she personally opposes it but favors the right of a woman to have one if she chooses. She also has said it is both the right and the duty of church officials to speak out on issues of concern to them, including abortion.

John Sasso, Ferraro's campaign manager, said, "I don't know what more she can say."

Almost at the same time that O'Connor was making his remarks on Sunday, President Reagan visited a Catholic religious shrine in Doylestown, Pa., where Cardinal John Krol of Philadelphia praised Reagan for providing food aid to Poland and supporting tax credits for parochial school patrons.

Ferraro strategists declined to dwell on the contrast of O'Connor's criticisms of Ferraro and Krol's virtual endorsement of Reagan. Privately, however, they questioned whether the two events were strictly coincidental.