Updated

Some of the most influential Catholic institutions in the country filed suit against the Obama administration Monday over the so-called contraception mandate, in one of the biggest coordinated legal challenges to the rule to date.

Claiming their "fundamental rights hang in the balance," a total of 43 plaintiffs filed a dozen separate federal lawsuits challenging the constitutionality of the requirement. Among the organizations filing were the University of Notre Dame, the Archdiocese of New York and The Catholic University of America.

The groups are objecting to the requirement from the federal health care overhaul that employers provide access to contraceptive care. The Obama administration several months ago softened its position on the mandate, but some religious organizations complained the administration did not go far enough to ensure the rule would not compel them to violate their religious beliefs.

A statement from the University of Notre Dame said the requirement would still call on religious-affiliated groups to "facilitate" coverage "for services that violate the teachings of the Catholic Church."

"The federal mandate requires Notre Dame and similar religious organizations to provide in their insurance plans abortion-inducing drugs, contraceptives and sterilization procedures, which are contrary to Catholic teaching," the statement said.

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Rev. John Jenkins, the president of Notre Dame, said in a message to the campus that the filing "is about the freedom of a religious organization to live its mission, and its significance goes well beyond any debate about contraceptives."

The contraception rule does include an exemption for religious organizations -- but that exemption does not cover many religious-affiliated organizations like schools and charities. Complaints about the narrowly tailored exemption prompted a stand-off between the Obama administration and religious groups earlier this year. As a compromise, the administration said insurers -- and not the religious-affiliated organizations themselves -- could be required to offer contraceptive coverage directly.

But many organizations were not satisfied with the plan. John Garvey, president of Catholic University, said in a statement Monday that "such a revision would not solve our moral dilemma." He argued that the cost of contraceptive coverage would still be "rolled into the cost" of a university insurance policy.

"In the end the university, its employees and its students will be forced to pay for the prescriptions and services we find objectionable," he said.

University of Notre Dame Law Prof. Richard Garnett said in a statement that the mandate could affect a range of religious institutions, including "schools, health care providers and social welfare agencies."

On a separate track, officials at a Florida Catholic university decided Monday to drop student health care coverage, becoming the second school this month to make that call. The decision at Ave Maria University was based in part on objections to the contraception rule, but also on projected increased premium costs tied to new rules in the federal health care overhaul.