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.

Based on early indications, the expected rule “would go a very long way to restoring religious freedom and conscience rights,” said Hillary Byrnes, assistant general counsel at the U.S. Conference of Catholic Bishops.

She said the rule couldn’t come soon enough. “We’ve been dealing with this mandate for over six years now,” she said. “A lot of people thought the administration would do something pretty quickly, yet here we are in August.”

Reproductive-rights activists say they will sue the Trump administration if it moves ahead with the rule, arguing that the change would unfairly impose employers’ beliefs on their workers and that the administration has cut regulatory corners in writing the policy.

“We are preparing various different legal theories to fight the rule very quickly,” said Mara Gandal-Powers, senior counsel at the National Women’s Law Center, an advocacy group. “We think we have a really strong claim.”

A spokeswoman for the Department of Health and Human Services declined to comment.

As a presidential candidate, Mr. Trump pledged support for Catholics and evangelical Christians who sued President Barack Obama and his top officials over the contraception requirement, contending that it forced them to violate their religious beliefs.

They also opposed a process, which the Obama administration dubbed an accommodation, in which an employer notifies the government of its unwillingness to cover contraceptives. That prompts the insurer administering the employer’s health benefits to assume the cost and administration of providing contraceptives, effectively cutting out the employer.

Religious employers challenged the policy in court, saying it made them complicit in a sin. The Supreme Court last year sent the case back to lower courts.

The Trump administration plans to offer the plaintiffs precisely what they sought: an exemption from the contraception requirement for all employers who want one, according to people familiar with the plan, ending the need for litigation.

Others regard the expected rule as a step back in a decadeslong fight to secure women’s access to contraceptive care.

Lawyers preparing potential legal cases for opponents of the change say that if the rule resembles the leaked draft, the policy could qualify as sex discrimination, since it would disproportionately affect women’s health care. They also plan to argue that leaving a decision on contraceptive coverage to employers could amount to religious discrimination by subjecting workers to the beliefs of their employers.

“If the rule says any employer can withhold this benefit from employees, then you have a whole set of questions about whether the government is enabling employers to impose their beliefs on others,” said Louise Melling, deputy legal director at the American Civil Liberties Union.

People familiar with the proposed rule say the Trump administration plans for it to take effect as it is published. Nicholas Bagley, a University of Michigan law professor who has analyzed much of the health-law litigation of the last six years, has said that could open the administration to lawsuits for implementing the rule without time for public comment and consideration.

“The argument they make is, ‘We’ve thoroughly vetted this issue, and we’re only making a minor change,’” he said. “If that was true, that argument would hold water. But that’s not true in this case.”

Write to Michelle Hackman at Michelle.Hackman@wsj.com and Louise Radnofsky at louise.radnofsky@wsj.com

Appeared in the August 17, 2017, print edition as ‘Contraceptive Rule to Be Reversed.’