The rule, implemented on January 20, requires religious-oriented groups such as charities, hospitals and universities, but not churches, to provide coverage for birth control as other health insurance providers must do.
The Catholic Church opposes most methods of birth control.
EWTN Global Catholic Network said it filed its case in U.S. District Court in Birmingham, Alabama against the U.S. Department of Health Human Services and other government agencies seeking to stop the imposition of the rule. The case asks the court to find the rule unconstitutional, it said.
The rule has sparked a firestorm of criticism from U.S. Catholic leaders and Republicans, including the party's presidential candidates, who have cast it as an assault by Obama on religious freedom.
EWTN Global Catholic Network calls itself the largest religious media network in the world, with satellite television, radio, and print news services, and other activities.
In another development, Archbishop of New York Timothy Dolan, who is the president of the U.S. Conference of Catholic Bishops, called on Obama to back off from the rule and said it contradicted assurances Obama gave him during a White House meeting in November.
Dolan, who has been designated by Pope Benedict for elevation to cardinal, said he now questions if he can work with Obama to settle concerns about the rule.
"Simply in the best American principles of freedom of religion, simply give a much more dramatically wide latitude to that religious exemption and protection of conscience and religious freedom, and you're not going to hear from us anymore," Dolan said on CBS's "This Morning" program.
"We can't have a government bureaucracy invading the privacy and the independence and autonomy and integrity that our constitution gives to religion," Dolan said.
The White House has said the rule aimed to strike a balance between Catholic Church doctrine and women's right to health care. It has promised to work with groups to implement the rule but has not backed away from it.
The issue has created a firestorm on a hot-button social issue during an election year that had been dominated until now by debates over the faltering economy.
Republicans were quick to portray Obama as leading an assault on religious liberty.
Republican House of Representatives Speaker John Boehner and Senate Minority Leader Mitch McConnell vowed to fight it.
Two senators, Republican Marco Rubio of Florida and Democrat Joe Manchin of West Virginia, introduced a bill to repeal it, although it was not expected to be brought to a vote in the Democratic-controlled Senate.
'NEGATIVE REACTION'
"I'm hoping that in this massive negative reaction to this ruling, I'm hoping that he'll go back to those assurances that he gave me," Dolan said.
"I hope he would understand that I'm a bit sceptical because ... he gave me promises. So I'm a little sceptical and I'm saying, wow, I hope I can continue to work with him," said Dolan.
"What's ultimately at stake is a First Amendment right and fundamental American value that has stood for two centuries," Boehner on Thursday told a conference of conservatives at a Washington hotel. "One thing is for certain: This attack on religious freedom cannot - and will not - stand."
The U.S. Constitution's First Amendment guarantees freedom of religion.
Some moderate Democrats facing election this year in conservative-leaning states - like Manchin in West Virginia and Tim Kaine, who is seeking a Senate seat in Virginia - have opposed the rule, although many Democrats have vocally backed Obama.
"My colleagues and I stand in solidarity with American women who have waited decades for equity in contraceptive coverage," U.S. Representative Nita Lowey said at a news conference with a dozen House Democrats to support the rule.
Twenty-eight states include similar requirements to Obama's rule in their insurance regulations, and Lowey said 335,000 houses of worship would be exempted.
"This rule in no way stops the church or any religious affiliated organization from discouraging women from using contraceptives based on moral arguments," she said.
Opinion polls indicate a majority of Americans, including a majority of Catholics, support Obama's decision.
A Public Religion Research Institute poll found 55 percent of Americans agree with requiring employers to provide health-care plans that cover contraception and birth control, including nearly six in 10 Catholics.
Many Catholic leaders have been outspoken in opposition. The Catholic Church rejects most forms of contraception such as birth control pills, but does condone the "natural" or "rhythm" method.
The regulation, required as part of the 2010 healthcare law, requires health insurance plans to cover basic preventative care for women.
The Obama administration, acting on recommendations from experts at the advisory U.S. Institute of Medicine, included birth control as part of that but exempted houses of worship.
Most employers and health plans have until August 1 to implement the new rule, but religious affiliated groups have until next year.