Bishop Michael Burbidge of the Raleigh diocese and Bishop Peter Jugis of Charlotte said in a prepared statement it was regrettable the president characterized the proposed amendment as a question of discrimination late last week.
The church leaders said Tuesday that Catholics support marriage as the union of a man and a woman, and that children have the right to a father and a mother in their lives as they grow.
Meanwhile, a Raleigh same-sex couple, who have been together for 20 years, told ABC11 that it's the bishops, not the president, who should stay out of the debate.
"I don't feel like he [Burbidge] has a right to weigh in on a legal issue when he's a religious figure," said Keith Turnmire.
Turnmire said Bishop Burbidge's statement on Amendment One is difficult to accept.
"It upsets me. It hurts my feelings," Turnmire said. "I feel like I'm being discriminated against."
The bishops pointed out the Catholic Church recognizes the personal dignity and equal worth of everyone.
"The amendment is an attempt to secure forever the definition of marriage," said Burbidge. "It is not an attack against any group of people or individuals."
The controversial amendment is set to go up for a vote on May 8.