MIAMI, Florida (CNN) -- An internationally known Catholic priest who was shown in photographs last week embracing a bathing-suit-clad woman on a Florida beach has admitted they had a two-year affair.

The Rev. Alberto Cutie was removed from his duties after pictures showed him bare-chested with a woman.

The Rev. Alberto Cutie -- sometimes called "Father Oprah" because of the advice he gave on Spanish-language media -- said Monday on CBS' "Early Show" that he is in love with the woman and is considering his options: Whether to break up with her or leave the priesthood and marry her. The woman, who has not been publicly identified, wants to get married, Cutie said.

The priest was removed from his duties last week at St. Francis De Sales Catholic Church in Miami Beach, Florida, and on the Radio Paz and Radio Peace networks.

"I take full responsibility for what I did, and I know it's wrong," he said Monday.

The photos of the Cuban-American priest, also known as "Padre Alberto," appeared on the cover of last week's TV Notas magazine and on eight inside pages. The cover says in Spanish: "Good God! Padre Alberto. First photos of a priest 'in flagrante' with his lover."

Other media outlets throughout Latin America, including the official Notimex news agency in Mexico, picked up the story, and it became an Internet sensation. Cutie has millions of followers in the Spanish-speaking world.

In a message posted on the Miami, Florida, archdiocese Web page last week, Archbishop John C. Favalora apologized to parishioners and radio listeners for what he called a "scandal."

"Father Cutie made a promise of celibacy and all priests are expected to fulfill that promise with the help of God," Favalora said. "Father Cutie's actions cannot be condoned despite the good works he has done as a priest."

Cutie expressed his regret in an online statement last week and again Monday on the CBS program.

"I deeply apologize to the Catholic community and especially to my bishop and to my brother priests who are faithful and who are committed to celibacy," Cutie said.

The priest said he believes in celibacy but thinks it should be optional. He said he had never had a sexual relationship with anyone other than the woman since leaving the seminary 15 years ago. Watch Father Cutie question the celibacy requirement »

"I don't support the breaking of the celibacy promise," Cutie said. "I understand fully that this is wrong.

"I don't want to be the anti-celibacy priest. I think that's unfortunate," he said. "I think it's a debate that's going on in our society, and now I've become kind of a poster boy for it. But I don't want to be that. I believe that celibacy is good, and that it's a good commitment to God. This is something I've struggled with. And something that I never expected to become a public debate."

He also talked about the woman, saying they have been friends for a long time and the attraction was there from early on, but it was not acted on until a couple of years ago. They have "both struggled" with the relationship, he said.

"She's also a woman of faith," Cutie said. "She's also somebody who cares about the priesthood, who cares about these things. So it hasn't been easy. And those who have helped me through this process know it hasn't been easy. Obviously, you know, through the photos, it looked like a frivolous thing on the beach, you know, and that's not what it is. It's something deeper than that."

Cutie was the first Catholic priest to host a daily talk show on a major secular television network, his information on the LinkedIn online professional network says.

In addition to his TV and radio appearances, he has written newspaper advice columns and a self-help book, "Real Life, Real Love."

Before being removed, he was president and general director of Pax Catholic Communications, home of Radio Paz and Radio Peace in Miami.

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