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He spoke about an exchange during his 2004 Illinois Senate campaign with a pro-life doctor who objected to a line on his campaign website that pledged to fight “right-wing ideologues who want to take away a woman’s right to choose.”

Mr. Obama said the exchange didn’t change his own views, but did cause him to change the website.

“I said a prayer that night that I might extend the same presumption of good faith to others that the doctor had extended to me,” he said. “Because when we do that — when we open our hearts and our minds to those who may not think like we do or believe what we do — that’s when we discover at least the possibility of common ground.”

Under the initial set of rules the administration announced, churches were exempt from having to provide insurance that covered contraceptives and some sterilization procedures, but their affiliated schools, charities and hospitals were not.

After several weeks Mr. Obama announced a new position he said would force insurers, not the Catholic organizations, to cover contraception costs. Notre Dame and other Catholic organizations rejected that, noting, among other things, that many large Catholic employers insure themselves, but said they would try to negotiate. But by last week, they said negotiations were stalling, and they filed suit.

Cardinal Timothy M. Dolan, the archbishop of New York and the president of the U.S. Conference of Catholic Bishops, accused the White House of “strangling” the church by treating religiously affiliated schools, hospitals and social service organizations as secular institutions.

“They tell us if you’re really going to be considered a church, if you’re going to be really exempt from these demands of government, you have to propagate your Catholic faith, and everything you do, you can serve only Catholics and employ only Catholics,” Cardinal Dolan said. “We’re like, ‘Wait a minute, when did the government get in the business of defining for us the extent of our ministry?’ “

Asked about Cardinal Dolan’s comments, White House spokesman Jay Carney said the administration is open to talking with church leaders, but he said Mr. Obama is committed to the contraceptives mandate.

“The policy the president has outlined meets two important objectives,” Mr. Carney said. “One, it ensures that women have access to important preventive services, including contraception. Two, it respects religious liberty. Under this policy, no religious university or religious organization will have to pay for or refer for contraceptive services, and no religious institution will have to provide these services directly.”

Recalling one of Mr. Obama’s first jobs in Chicago with a church-based organization funded in part by Catholic charities, Mr. Carney said the president has a deep respect for Catholic institutions.

“So he is very well aware of the important role that institutions like that play in our society, the fact that they can provide services that can be more helpful than any government program,” Mr. Carney said. “He believes strongly in religious liberty, and the need to protect it. He also believes strongly in the need to give women access to, and provide preventive services that are essential, including contraception.”