The law bars such funds from entities that perform or promote abortions.
Judge Jeffrey Sutton wrote the opinion for an 11-6 majority, saying the judges rejected the contention by two Planned Parenthood affiliates that the Ohio law imposes an unconstitutional condition on public funding.
"The affiliates are correct that the Ohio law imposes a condition on the continued receipt of state funds. But that condition does not violate the Constitution because the affiliates do not have a due process right to perform abortions," Sutton wrote.
Sutton wrote for the majority that while Planned Parenthood contends that the Ohio law will unconstitutionally deprive women of the right to access abortion services without undue burden, that conclusion is premature and speculative because Planned Parenthood has stated it will continue to provide abortion services.
Judge Helene White wrote the dissenting opinion, saying such laws allow targeting of abortion providers who are "merely a proxy for the woman and her constitutional rights" and are trying to make them "cry uncle." She said using the majority's reasoning, "the government can do almost anything it wants to penalize abortion providers so long as they resist the coercion and continue to perform abortions."
Planned Parenthood leaders said Tuesday the funding has helped provide tests for sexually transmitted diseases, cancer screenings, domestic violence education, and efforts to reduce infant mortality.
Dr. Leana Wen, the organization's national president, said the ruling will "roll back the gains to public health — harming women's health, children's health and the health of families across Ohio." She in a statement called it "unconscionable" that politicians continue seeking to restrict access to essential health care.
Planned Parenthood didn't say immediately whether it will seek to appeal to the U.S. Supreme Court
A U.S. district court ruling had agreed with Planned Parenthood that denying the organization funding if it continued to perform abortions violated the organization's right to due process, and that denying funding for promoting abortion violated its free speech rights.
A three-judge panel of the 6th Circuit appeals court agreed with the lower-court ruling for an injunction against the 2016 law, prompting then-Attorney General Mike DeWine last year to seek a full-court hearing. The Republican took office this year as governor, succeeding Republican John Kasich.
DeWine's office said he was "pleased by today's decision as he has long believed that the people of Ohio, through its state legislature, have the right to decide what it funds and what it doesn't fund."
David Pepper, Ohio's Democratic Party chairman, said the ruling hurts Ohio kids and families, but that DeWine chose to side with "anti-abortion extremists."
Under the U.S. Supreme Court's 1973 Roe v. Wade ruling, women have a constitutionally protected right to terminate a pregnancy before a fetus is able to survive outside the womb. Anti-abortion groups and politicians around the country have continued efforts to undermine that ruling or get it reversed by a Supreme Court with two new justices nominated by Republican President Donald Trump.
Planned Parenthood is a national target because of its role as the largest U.S. abortion provider.
Associated Press writer Andrew Welsh-Huggins contributed in Columbus.
Contact Dan Sewell at https://www.twitter.com/dansewell