“The makeup of the Supreme Court is probably the most conservative we’ve seen in a generation, and that certainly emboldens those of us who deeply desire that Roe v. Wade be overturned,” said Jamieson Gordon, the spokeswoman for Ohio Right to Life, which opposes abortion.

Since John Kasich became governor of Ohio in 2011, the state has enacted more than 20 abortion restrictions and the number of full-service abortion clinics there has fallen to seven from 16, according to Kellie Copeland, the executive director of NARAL Pro-Choice Ohio, an abortion rights group that plans to fight the new law.

While the measure is the first major abortion restriction signed by Mr. DeWine, who took office in January, his support for the bill was hardly a surprise to abortion rights supporters given his role as attorney general under Mr. Kasich, a fellow Republican.

“The reaction from our supporters has been exactly what we knew it would be, which is defiance,” Ms. Copeland said. “We are not accepting the barriers that these politicians are trying to put on our bodily autonomy.”

Nationally, more than 300 abortion restrictions were introduced in the first three months of this year, according to the Guttmacher Institute, which described the flurry of legislative activity as a “surge.” At the same time, though, some state lawmakers have sought to expand abortion rights.

In January, Gov. Andrew M. Cuomo of New York, a Democrat, signed into law a bill that permits abortion after the 24th week of pregnancy as long as the fetus is not viable or the abortion is necessary to protect the mother’s life or health.

“The events of the last several months absolutely validate the decisive actions taken by New York to legally protect abortion — and more states must follow suit so that people can continue to access the care they need when they need it,” Elizabeth Nash, senior state issues manager at the Guttmacher Institute, said in a statement.

Among the restrictions introduced this year was a bill in Texas that appeared to have stalled this week and would have criminalized abortions outright, potentially allowing women and physicians to receive the death penalty.