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The Obama administration, seeking to rein in a runaway political furor over birth control and religious liberty, is set to announce a possible compromise on Friday that is meant to calm ire from the right about a new administration rule that would require health insurance plans — including those offered by Roman Catholic hospitals, universities and charities — to offer free birth control to female employees.

Administration officials called the expected announcement an “accommodation” that they said sought to demonstrate respect for religious beliefs. It will be similar to the path taken in several other states — particularly Hawaii — that have similar rules.

But administration officials also acknowledged that it would likely not mollify the Catholic bishops who have waged war against the rule or, for that matter, Congressional Republicans and candidates on the presidential campaign trail who have joined the fight. At most, the compromise could potentially help President Obama shore up support among wavering Democrats, who have also expressed doubt about the rule, along with more liberal religious organizations and charities, who oppose the rule but not as vehemently as the Catholic leadership.

Emulating Hawaii, where the rule is in effect, would mean that employees at religious institutions that do not offer free contraception in the health insurance plan can get birth control through side benefits, which the employees nominally pay for but which often end up being free.