Updated, 6:12 p.m.
(CBS News) The spat between Catholic leaders and the Obama administration over its contraception policies is heating up again, with one of the nation's most prominent Catholic leaders charging that the White House is "strangling" the church over the matter.
Cardinal Timothy Dolan told "CBS This Morning" Tuesday that the compromise reached earlier this year is not sufficient because the exemptions made for churches are too restrictive.
"They tell us if you're really going be considered a church, if you're going to be really exempt from these demands of the government, well, you have to propagate your Catholic faith and everything you do, you can serve only Catholics and employ only Catholics," 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," Dolan said.
More than 40 Catholic organizations sued the Obama administration Monday over a government requirement that most employers provide birth control coverage as part of their employee health plans.
The U.S. Health and Human Services Department adopted the rule to expand health care for women. Last year, an advisory panel from the Institute of Medicine, which advises the federal government, recommended including birth control on the list of covered services, partly because it promotes maternal and child health by allowing women to space their pregnancies.
However, faith leaders from across religious traditions protested, saying the mandate violates religious freedom. The original rule includes a religious exemption that allows houses of worship to opt-out of the mandate, but keeps the requirement in place for religiously affiliated charities.
In response to the political furor, President Obama offered to soften the rule so that insurers would pay for birth control instead of religious groups. However, the bishops and others have said that the accommodation doesn't go far enough.
Dolan also criticized Georgetown University's decision to invite Health and Human Services Secretary Kathleen Sebelius to speak to graduates of its school of public policy last week because of her role in formulating the policy.
"Well, I do think that's a problem. Georgetown is the oldest Catholic university in the country. Part of Catholic identity is to be in union with the bishops," Dolan said.
"When they would invite someone that is so dramatically at odds with one of the central tenets of the faith, that does bother us," Dolan said.
Sebelius is a practicing Catholic and mother and spouse of Georgetown graduates. Georgetown University President John DeGioia defended the university's decision to invite Sebelius as evidence the university "is committed to the free exchange of ideas."
The Associated Press contributed to this report.