WASHINGTON—The Trump administration is poised to issue a rule unwinding an Obama-era requirement that employee health benefits include contraception, which will spark a fresh round of litigation over an issue that has been before courts for six years.

Federal health officials are expected to finalize a regulation that would allow employers with religious or moral objections to birth control to omit coverage for contraception from their workers’ plans, according to two people familiar with its contents. The regulation closely mirrors an earlier, leaked draft, they said.

The Supreme Court has ruled, in a case brought by the arts-and-crafts chain Hobby Lobby, that “closely held” private companies can invoke religious objections to avoid covering contraception.

The Trump administration rule would allow a much broader set of employers to opt out of offering coverage for birth control, making moot a “workaround’’ designed by the Obama administration that allowed women in some cases to obtain coverage even if their employers had declined to offer it directly.

The rule would fulfill a promise by President Donald Trump to social conservatives, who backed his candidacy but have been frustrated by the pace of his administration has moved to address one of their most significant grievances.