(CNN) – An adjustment to a controversial federal rule requiring employers cover contraception in their health insurance plans was labeled "dubious" by an influential group of Roman Catholic bishops on Wednesday.
The rule in question mandated all employers, including religiously affiliated organizations like hospitals and colleges, provide free contraception to employees through health insurance plans. Churches were exempted from the law.
After uproar from conservatives and religious groups, President Barack Obama announced an accommodation to the rule. Under the new plan, insurers will be required to offer complete coverage free to women instead of the religious institutions themselves.
On Wednesday the United States Conference of Catholic Bishops said the new rule remained "unspecified and dubious," and said they would seek to engage in conversations with members of Obama's administration to seek a more attractive alternative.
"We will continue to accept any invitation to dialogue with the executive branch to protect the religious freedom that is rightly ours," the bishops said. "We will continue to pursue legislation to restore the same level of religious freedom we have enjoyed until just recently. And we will continue to explore our options for relief from the courts, under the U.S. Constitution and other federal laws that protect religious freedom."
The group also attempted to push back on criticism from liberals that their opposition to the contraception rule was akin to restricting access to forms of birth control.
"This is not about access to contraception, which is ubiquitous and inexpensive, even when it is not provided by the church's hand and with the church's funds," the group wrote.
The statement continued, "Indeed, this is not about the church wanting to force anybody to do anything; it is instead about the federal government forcing the church - consisting of its faithful and all but a few of its institutions - to act against church teachings."
Responding to the bishops, Catholic League President Bill Donohue said the statement "leaves nothing on the table."
"It debunks many myths about this issue: it is not about contraception; it is not just about Catholic religious rights; it is not about the Catholic Church trying to impose its will on others," Donohue wrote. "It is about the federal government trying to impose its agenda on us."
Thomas Reese, a Jesuit priest at Georgetown University, said the bishops' statement used "strong and uncompromising" language while not becoming inflammatory.
"The statement's reference to the administration's adaptation as 'unspecified and dubious' highlights the bishops' distrust of the White House and HHS," Reese said. "The bishops do not believe the administration's promises to fix the problem for faith-based organizations and self-insured plans."
Reese pointed out a flaw in the bishops' argument that employers who feel their conscience was violated by providing contraception coverage should be exempted from the law.
"The statement infers that religious liberty is an absolute right that cannot be restricted," Reese said. "If this were true, Mormons and Muslims could practice polygamy and those who believe God demands the separation of the races should be exempted from civil rights legislation."
-CNN’s Eric Marrapodi contributed to this report.