Lawmakers in Oklahoma on Tuesday approved a near-total ban on abortion, making it the latest Republican-led state to forge ahead with stringent abortion legislation as the Supreme Court weighs a case that could overturn Roe v. Wade later this year.

The measure, Senate Bill 612, would make performing an abortion “except to save the life of a pregnant woman in a medical emergency” a felony punishable by up to 10 years in prison or a fine of $100,000.

The Oklahoma House voted 70 to 14 to send the bill, which passed the Senate last year, to Gov. Kevin Stitt, a Republican whose office responded by noting that Mr. Stitt vowed in September to sign “every piece of pro-life legislation” that came to his desk.

If Mr. Stitt signs the bill, it would take effect on Aug. 26, according to the Senate clerk’s office.

Its passage came after Oklahoma became a major destination for women from Texas who were seeking abortions after that state enacted a law banning the procedure after about six weeks, a very early stage of pregnancy.

“If allowed to take effect, S.B. 612 would be devastating for both Oklahomans and Texans who continue to seek care in Oklahoma,” a coalition of abortion rights groups, including the A.C.L.U. of Oklahoma and Oklahoma Call for Reproductive Justice, said in a statement.

“Nearly half of the patients Oklahoma providers are currently seeing are medical refugees from Texas,” the groups said. “Now, Oklahomans could face a future where they would have no place left in their state to go to seek this basic health care.”

Representative Jim Olsen, a Republican from Roland, and the House author of the bill, said the measure was enacted in anticipation of a pending Supreme Court decision on a Mississippi law that bans abortions after 15 weeks of pregnancy.

If the court upholds that law, it could upend Roe v. Wade, the 1973 decision that established a constitutional right to abortion and that prohibited states from banning the procedure before fetal viability, or around 23 weeks.

From Florida to Idaho, Republican-led state legislatures have been operating as though Roe has already been struck down, advancing restrictions that aim to make abortion illegal in as many circumstances as possible.

“Obviously, I’m thrilled because we have the potential of seeing many lives of babies saved — part of that depends on future court rulings” like the one in the Mississippi case, Dobbs v. Jackson Women’s Health Organization, Mr. Olsen said.

He said the bill passed without any floor debate.

“Nobody debated and nobody asked any questions,” he said. “I was actually kind of shocked.”

Mallory Carroll, a spokeswoman for the Susan B. Anthony List, an anti-abortion group, said Oklahoma, as one of “the most pro-life states in the country,” was following other states in enacting laws to restrict abortion as much as possible.

“This latest bill passage is yet another sign of the continued pro-life momentum we’re seeing nationwide as lawmakers and pro-life Americans await a decision from the Supreme Court in the Dobbs case,” Ms. Carroll said.

Emily Wales, interim president and chief executive of Planned Parenthood Great Plains, said the bill was one of a series of anti-abortion measures advancing in Oklahoma, including one that mirrors the Texas law, which effectively deputized citizens to sue clinics and others who violate the law.

She said anti-abortion members of the Oklahoma House approved the bill as lawmakers who support abortion rights were outside the State Capitol, speaking at a “Bans off Oklahoma” rally.

Planned Parenthood, which operates two of the four abortion clinics in Oklahoma, planned to challenge the legislation in court, Ms. Wales said.

“This ban is more in line with the traditional bans that have been blocked in the past,” she said. “So we are fairly confident that, as long as Roe remains the law of the land, there is a path to blocking this.”

Rebecca Tong, co-executive director of Trust Women, which operates a clinic that provides abortions in Oklahoma City, said the clinic “will remain open so long as we can still be of service to the people of Oklahoma.”

“We will not be deterred from providing compassionate health care to our patients — many of whom are our neighbors, colleagues, and family,” Ms. Tong said in a statement.