Archbishop Timothy Dolan added another chapter Tuesday morning to the ongoing disagreement between some Catholic bishops and the White House, feeling that the Obama administration is "strangling" churches over the birth control mandate exemption.

Appearing on CBS This Morning, Dolan was again adamant with his belief that the exemption made for churches was too "choking" because the exemption defines religious institutions as those who put faith into practice, but excludes their schools, hospitals and charities.

"What we're worried about now is the exemption given to the churches is so strangling and so narrow, and it's also presumptuous in that the bureau of the federal is attempting to define for the church the extent of its ministry and its ministers," Dolan said, who is president of the U.S. Conference of Catholic Bishops. "It's that exemption, it's the straight jacketing, handcuffing exemption, characteristic of that exemption, Charlie (Rose) and Erica (Hill), that we find very dangerous."

On Monday, 43 Catholic institutions filed 12 separate lawsuits against the Obama administration over the birth control rule. A recent CBS News/New York Times poll revealed that 61 percent of Americans supported the rule.

WATCH: Video from CBS, which was broadcast on May 22, 2012.