WASHINGTON -- After months of criticism and legal challenges, President Barack Obama’s administration proposed Friday that religious institutions no longer be required to provide their employees with health insurance coverage for birth control.

Nonprofit organizations that had objected to the mandate on moral grounds, including hospitals and universities, would be able to offer plans that don’t cover contraceptives, while their employees could enroll in separate insurance policies that would cover free birth control.

The contraceptives’ cost would be paid for through long-term health benefits of preventative coverage and fees insurers pay to participate in the health exchanges set up as part of the federal health care law passed in 2010, according to administration officials.

“The administration is taking the next step in providing women across the nation with coverage of recommended preventive care at no cost, while respecting religious concerns,” Health and Human Services Secretary Kathleen Sebelius said.

The proposal – the second change to quell criticism in a year – is part of a set of recommendations announced Friday that might be tweaked further after public input. But it still fell short of satisfying critics.

The White House has struggled for two years to strike a balance between its desire to provide free birth control through health insurance with a need to accommodate the religious freedom of employers who provide insurance but object to contraception on moral grounds.

White House officials declined to answer a series of questions about the recommendations Friday, merely saying that they reflected Obama’s views.

“The president has been very clear about his views on this,” White House spokesman Jay Carney said. “He’s been very clear about what he believes are two compelling interests. . . . And he has instructed those who work for him on this issue to be cognizant of those criteria.”

Women’s’ groups applauded the move, saying it would ensure that women have access to contraceptives as part of basic health care coverage.

“The principle is clear and consistent,” said Cecile Richards, the president of the Planned Parenthood Federation of America. “This policy makes it clear that your boss does not get to decide whether you can have birth control.”

Religious groups were still dissatisfied with the proposal, which also would expand the definition of religious institutions.

The U.S. Conference of Catholic Bishops, which has been sharply critical of the mandate, said it was reviewing the changes. Others assailed them.

The Becket Fund for Religious Liberty, which has filed several lawsuits challenging the mandate, said it was “extremely disappointed” with what it called an inadequate proposal.

Kyle Duncan, the fund’s general counsel, suggested that “very, very few” organizations, if any, are likely to get any relief from the proposed changes. “We were hoping for much, much more from the administration,” Duncan said, noting that the proposal would have no effect on for-profit organizations and family-owned businesses.

The contraceptive mandate spurred more than 40 lawsuits nationwide, filed by employers ranging from the Roman Catholic Archdiocese of Miami to the University of Notre Dame. Judges have dismissed many of the legal challenges, reasoning that lawsuits are premature because the mandate hasn’t kicked in yet.