Ohio moved one step closer to becoming the next big test case in the nation’s fight over abortion, after supporters of a measure that would ask voters to establish a right to abortion in the state’s Constitution this week said they had filed more than enough signatures to put it on the ballot in November.

Ohioans United for Reproductive Rights said on Wednesday that it had collected roughly 710,000 signatures across all of the state’s 88 counties over the last 12 weeks. Under state law, the coalition needed 413,466 to qualify for the ballot. State election officials now have until July 25 to verify the signatures.

Supporters of abortion rights are turning to ballot measures in the aftermath of the ruling last year by the United States Supreme Court overturning Roe v. Wade, which for 50 years had guaranteed a right to abortion in the federal Constitution. They are betting on polls showing that public opinion increasingly supports some right to abortion, and opposes the bans and stricter laws that conservative state legislatures have enacted since the court’s decision.

Voters in six states, including conservative ones such as Kentucky and Kansas, voted to protect or establish a right to abortion in their constitutions in last year’s elections, and abortion rights advocates in about 10 other states are considering similar plans.

Anti-abortion advocates have become more reluctant to use ballot measures, but that does not mean they have stopped pushing to enact stricter limits. In Iowa, where the State Supreme Court last month declined in a deadlocked vote to lift a block on a near-total abortion ban, anti-abortion advocates have explored adding an amendment to the state’s Constitution saying that there is no right to abortion.

On Wednesday, Gov. Kim Reynolds, a Republican, led a different approach, announcing that she was ordering a special session of the Legislature to convene next week with the sole purpose of enacting another ban. The court’s decision, she said, “disregards the will of Iowa voters and lawmakers.”

In Ohio, at a news conference after delivering the truckload of signed petitions on Wednesday, members of Ohioans United for Reproductive Rights expressed confidence about a November vote.

“We know from providing 50 years of abortion care that people from every corner of this state need this service,” said Sri Thakkilapati, a founder of the group and the executive director of the Cleveland abortion clinic Preterm. “And we know from collecting signatures in every single one of Ohio’s 88 counties that people support this right.”

But the November ballot measure is not the only one that will carry big stakes for the future of abortion in Ohio. Republicans who oppose abortion rights — and who control the state’s General Assembly — have proposed another measure that would make it harder to pass the ballot measure.

Republican leaders in the legislature have placed a measure on the primary ballot in August that would raise the threshold required to pass any ballot measure amending the state’s Constitution to 60 percent, from a simple majority. They aimed that measure — which would require 50 percent of voters to pass — squarely at the abortion question. Earlier this year the same Republicans passed a law eliminating almost all August elections, arguing that they are expensive and have such low turnout as to be undemocratic.

While summer elections tend to have low turnouts and favor those sponsoring the measures, Republicans in Kansas who attempted to strike a right to abortion from the state’s Constitution last August failed, with an unexpectedly high proportion of residents turning out to reject it. The August measure in Ohio, however, will not specifically mention abortion, and it’s not clear that abortion rights advocates will be able to energize their supporters as effectively as their counterparts in Kansas did.

Michael Gonidakis, the longtime president of Ohio Right to Life, cast doubt on the significance of the signatures delivered by abortion rights supporters this week. He noted that a group that attempted an amendment on criminal justice in 2018 submitted more than 730,000 signatures, but fewer than half were declared valid. And 63 percent of voters ultimately rejected the proposal.

The Republican-led legislature in Ohio passed a law in 2019 banning abortion after six weeks of pregnancy — before many women know they are pregnant — with exceptions to save the life of the mother or prevent “major impairment” of a bodily function, but not for rape or incest. That law took effect after Roe was overturned, but a county court judge put a hold on it, saying that the Ohio Constitution provided a “fundamental right to abortion,” in part because it granted equal protection and benefit to women. That leaves abortion legal up until 22 weeks of pregnancy.

The ballot measure would amend the Constitution to add “the Right to Reproductive Freedom with Protections for Health and Safety Amendment,” which in many ways resembles the protections established by Roe.

It would establish a right to abortion but allow the procedure to be prohibited after the fetus is viable outside the womb, generally around 23 or 24 weeks. It would allow limits on abortion before viability so long as those laws used the “least restrictive means to advance the individual’s health” according to “widely accepted and evidence-based standards of care.”

In a statement, the leaders of Ohioans United for Reproductive Rights declared that the amendment would “ensure patients and doctors, not government extremists, are in control of making private medical decisions.”

But in a flurry of statements and Twitter posts, anti-abortion groups hinted that they intended to argue that the amendment is extreme.

The anti-abortion coalition Protect Women Ohio insisted that signature collectors had lied about the amendment, and argued that it would “strip parents of their rights, permit minors to undergo sex-change operations without their parents’ knowledge or consent and allow painful abortion on demand through all nine months,” despite the language allowing the state to prohibit abortions after viability.

In a Public Religion Research Institute poll in December, 66 percent of Ohio residents said abortion should be legal in all or most cases, up from 56 percent in December 2018.