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The Supreme Court has agreed to hear another challenge to President Obama's health care law -- this time on the so-called contraception mandate.

The justices announced Tuesday that they will take up the long-running dispute over whether businesses can use religious objections to avoid a requirement in the law to cover birth control for employees. Despite the 2012 high court ruling that upheld most of the Affordable Care Act, dozens of lawsuits have continued to proceed from companies asking to be spared from having to cover some or all forms of contraception.

The matter has divided the lower courts. The Supreme Court could consider the challenge as early as March.

The court will consider two cases. One involves Hobby Lobby Inc., an Oklahoma City-based arts and crafts chain with 13,000 full-time employees. Hobby Lobby, owned by founder David Green and his family, won in the lower courts.

"This is a major step for the Greens and their family businesses in an important fight for Americans' religious liberty," said Kyle Duncan, general counsel of the Becket Fund for Religious Liberty which is representing Hobby Lobby. "We are hopeful that the Supreme Court will clarify once and for all that religious freedom in our country should be protected for family business owners like the Greens."

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    The other case being considered is an appeal from Conestoga Wood Specialties Corp., a Pennsylvania company that employs 950 people in making wood cabinets. Lower courts rejected that company's claims.

    The announcement from the high court comes as the president's signature domestic policy achievement is weathering a storm of criticism, over the troubled insurance website and a wave of policy cancellations.

    The White House put out a statement Tuesday defending the requirement that employers offer access to contraception coverage.

    "The health care law puts women and families in control of their health care by covering vital preventive care, like cancer screenings and birth control, free of charge," the statement said. "We believe this requirement is lawful and essential to women's health and are confident the Supreme Court will agree."

    The statement noted that the administration already tried to accommodate religious organizations, with a change last year that would have insurers sell those policies directly to their employees. But some groups said the change doesn't go far enough. And non-religious organizations were also left out of the arrangement.

    The Associated Press contributed to this report.