AUGUSTA — Abortion providers and the American Civil Liberties Union filed a lawsuit against the state Tuesday in a bid to overturn a longstanding rule limiting low-income women’s access to a state-funded abortion.

It’s buried deep within a set of rules developed in 1981 and last revised in 2010, before Gov. Paul LePage took office. However, it could set up a politically charged court fight with the anti-abortion Republican and his administration.

The lawsuit against the Maine Department of Health and Human Services was filed Tuesday morning in Cumberland County Superior Court on behalf of the state’s three abortion providers, Planned Parenthood of Northern New England, Mabel Wadsworth Women’s Health Center in Bangor and Maine Family Planning in Lewiston.

The challenged rule only allows women enrolled in MaineCare — the state’s version of Medicaid, the federal-state health care program for low-income people — to have an abortion paid for by MaineCare in cases of rape, incest and if their life is in danger.

The ACLU and Planned Parenthood say the rule violates Maine law and the state constitution, which enumerates the rights to pursue happiness and equal protection under the law by only affecting the ability of low-income women to get an abortion and not those with private insurance.

“We think, however you feel about abortion, it’s not fair to have a two-tiered system,” said Zachary Heiden, a lawyer for the ACLU of Maine.

The Maine Department of Health and Human Services and LePage’s office didn’t immediately respond to a request seeking comment, but the governor is firmly anti-abortion, saying at a campaign event last September that he’s against “killing babies as a form of contraception.”

The rule is a rare example of restrictive abortion policy in Maine, which has some of the most permissive abortion laws in the country, according to the pro-choice Guttmacher Institute. But Maine is in the nation’s mainstream on public abortion funding.

The Hyde Amendment limits federal money from being spent on abortion except in cases of rape, incest or if the life of the mother is endangered. While states can choose to fund other abortions themselves, Maine is one of 32 that has chosen to stick roughly to federal law, according to Guttmacher.

One-third of the Mabel Wadsworth Center’s 1,400 patients per year — 400 of whom receive abortion services — are either on MaineCare or would qualify if they got pregnant, and issues with abortion access have been exacerbated as the center sees “more and more people struggling to make ends meet,” said Andrea Irwin, the center’s executive director.

“We think it’s important that no matter how much money you make, you have access,” she said.