"It was very candid. I would say there were areas of agreement and disagreement," Dolan told reporters at the bishops gathering.
"But I would say this: that I found the president of the United States to be very open to the sensitivities of the Catholic community that were worried about an intrusion into religious liberty."
Dolan said Obama was "very sensitive" to the bishops' concerns over gay marriage and insurance mandates to provide artificial birth-control coverage as part of the new health-care reform law.
"He was very ardent in his desire to assure me that this is something he will look long and hard at. And I left there feeling a bit more at peace about this issue than when I entered."
That sentiment, coming after Dolan's first face-to-face meeting with Obama since he was elected to lead the bishops last year, marks a sea change from tense relations between the U.S. hierarchy and the administration.
Beyond the administration's decision not to enforce a federal ban against gay marriage, the bishops are worried that state efforts to legalize gay marriage or allow civil unions will force them to choose between the law and their moral beliefs.
That conflict grew deeper in August when the Department of Health and Human Services announced regulations that would require all health-insurance policies to provide contraception at no extra cost. Catholic bishops and others say an exemption for religious groups is so narrow as to be meaningless.
The bishops say the decisions represent a pervasive hostility to religious groups, and they've established a new Committee for Religious Liberty to defend the church's interests in Washington.
The policy jousting has been matched by escalating rhetorical broadsides from the bishops. Cardinal Francis George of Chicago, Dolan's immediate predecessor as head of the bishops conference, has called Obama's White House "the most secularist administration in history."
Last week, Auxiliary Bishop James D. Conley of Denver told an anti-abortion group in Dallas that he believes the U.S. "is becoming what I would call an 'atheocracy' a society that is actively hostile to religious faith and religious believers."
The fight over religious freedom is a central theme of the bishops' fall meeting. On Monday, Bishop William E. Lori of Bridgeport, Conn., head of the new religious-liberty committee, told the bishops that "both law and culture are indeed establishing unreligion as the religion of the land."
"This and more have led to dramatic and immediate threats to religious liberty across our land," Lori warned.
But Lori and Dolan pointed out that they believe the church is facing strong cultural headwinds, not just a hostile administration.
"We see in our culture a drive to neuter religion," Dolan said, warning of a campaign backed by "well-financed, well-oiled sectors, to push religion back into the sacristy."