WASHINGTON — The Supreme Court will consider allowing the Trump administration to enforce rules that allow more employers to deny insurance coverage for contraceptives to women.

The justices agreed Friday to yet another case stemming from President Barack Obama’s health care overhaul, this time about cost-free birth control. The court probably will hear arguments in April.

The high court will review an appeals court ruling that blocked the Trump administration rules because it did not follow proper procedures. The new policy on contraception, issued by the Department of Health and Human Services, would allow more categories of employers, including publicly traded companies, to opt out of providing no-cost birth control to women by claiming religious objections.

The policy also would allow some employers, though not publicly traded companies, to raise moral objections to covering contraceptives.

Employers also would be able to cover some birth control methods, and not others. Some employers have objected to covering modern, long-acting implantable contraceptives, such as IUDs, which are more expensive and considered highly effective in preventing pregnancies.

Even though the Trump rules remain blocked, a ruling by a federal judge in Texas in June already allows most people who object to covering contraception to avoid doing so.

The issue in all the cases is the method originally adopted by the Obama administration to allow religiously affiliated organizations to opt out of paying for contraception while making sure that women under their plans would not be left with the bill.

Some groups complained that the opt-out process violated their religious beliefs and wanted to be relieved of even signaling their religious objection.

The share of female employees paying their own money for birth control pills has plunged to under 4 percent, from 21 percent, since contraception became a covered preventive health benefit under the Obama-era health law, according to the Kaiser Family Foundation.

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