DAKAR, Senegal — The clinic, tucked discreetly inside the student health center on the University of Dakar campus, prescribes birth control pills, hands out condoms and answers questions about sex that young women are nervous about asking in this conservative Muslim country.

The clinic performs no abortions, nor does it discuss the procedure or give advice on where to get one. Senegal, by and large, outlaws abortion. But for other health services like getting contraceptives, said Anne Lancelot, the Sahel director at the organization that runs the clinic, “there is a very high demand.”

Now, under a Reagan-era policy revived by President Trump, the clinic may no longer be able to count on aid money from the United States Agency for International Development, part of a ban on providing abortion counseling overseas that could curtail a broad range of health services, including those that go well beyond abortion.

Known as the Mexico City policy — and by its critics as the global gag rule — the abortion policy prohibits organizations abroad from using American aid to talk about abortion as a method of family planning. Anti-abortion groups like the Family Research Council have welcomed Mr. Trump’s decision, saying it is consistent with “his campaign promise that he will protect taxpayers from having to pay for abortions.”