WASHINGTON — Mindful of the clock ticking down to a Trump presidency, the Obama administration issued a final rule on Wednesday to bar states from withholding federal family-planning funds from Planned Parenthood affiliates and other health clinics that provide abortions. The measure takes effect two days before the Jan. 20 inauguration of Donald J. Trump.

The rule was proposed three months ago, when many Democrats assumed the next president would be Hillary Clinton; she presumably would have promoted the rule’s completion if it were still pending. It requires that state and local governments distribute federal funds for services related to contraception, sexually transmitted infections, fertility, pregnancy care, and breast and cervical cancer screening to qualified health providers, regardless of whether they also perform abortions.

Mr. Trump has sent mixed messages on Planned Parenthood’s work, supporting its health-related services other than abortion. Yet with backing from Republican leaders in Congress, he has indicated he will undo many Obama administration rules and regulations, especially last-minute additions. In this case, however, unraveling the new rule would first require a time-consuming process, according to the Department of Health and Human Services.

The department began the rule-making effort in September after more than a dozen Republican-dominated states moved in recent years to “defund” Planned Parenthood by blocking clinics from receiving public money. Those funds included so-called Title X money — named for the federal family-planning program — as well as Medicaid reimbursements for treating low-income patients.