A sweeping set of abortion restrictions adopted by the Texas state Senate on Saturday is the latest in a series of state-level political fights triggering a frenzy of legal action that could determine how much access to abortion services American women have in the future.

Abortion opponents hope that eventually some of cases will reach the U.S. Supreme Court.

In recent months, abortion has moved to the political center stage as an increasing number of Republican-controlled legislatures have enacted new abortion restrictions. The result is a flurry of activity by both opponents and supporters of abortion rights that has made the abortion debate more politically volatile than it has been in many years.

So far this year, state legislatures have enacted more than 40 measures to restrict or control access to abortion, according to the nonprofit Guttmacher Institute, and proponents of those measures acknowledge that they are deliberately inviting legal challenges in the hope that the cases will land in federal courts and produce stricter limits on abortion nationwide.

North Dakota Gov. Jack Dalrymple (R) — who signed legislation in late March restricting abortions as soon as a heartbeat is detectable, which can be as early as six weeks — said at the time: “Although the likelihood of this measure surviving a court challenge remains in question, this bill is nevertheless a legitimate attempt by a state legislature to discover the boundaries of Roe v. Wade.”

Abortion rights supporters said the recent rush of activity has strengthened their argument that women’s access to the procedure is now under serious threat. In response, they have filed dozens of lawsuits aimed at blocking some of the highest-profile bills on the grounds that they place an undue burden on women seeking abortions before the point where the fetus is viable.

Saturday morning’s vote in Texas came after a standoff that lasted several weeks. The state Senate voted 19 to 11 to adopt a measure that would ban abortions after 20 weeks and require physicians who perform abortions to have admitting privileges at a nearby hospital. It also requires all abortions to take place in fully equipped surgical centers.

Only six of the state’s 42 abortion clinics meet the new requirements, and abortion rights advocates say the legislation means dozens will be shuttered.

“Now people really understand this is national trend, this is a wave,” said Louise Melling, director of the American Civil Liberties Union’s Center of Liberty. “It’s an effort to change the landscape across the country for abortion, even if it’s state by state.”

Texas Gov. Rick Perry (R) has been a strong supporter of the proposed new restrictions in his state and is expected to sign the legislation, which is scheduled to take effect Aug. 1. But when and whether that happens is likely to be decided by the courts.

Planned Parenthood President Cecile Richards said Saturday that her group was “evaluating litigation options” regarding the Texas law.

“We believe provisions of this bill are unconstitutional. Similar provisions enacted elsewhere have been enjoined by federal and state courts,” Richards said, promising to “take appropriate steps to prevent these provisions from taking effect and endangering the health of women in Texas.”

So far, federal and state judges have largely accepted abortion rights activists’ argument that it is unconstitutional to ban the procedure before viability of the fetus. The 1973 Supreme Court decision Roe v. Wade leaves that determination to the individual’s doctor, which is usually interpreted as 24 weeks after fertilization.

But courts have been less willing to strike down other restrictions, such as ones requiring abortion clinics to conduct costly upgrades, perform ultrasounds on their patients before doing an abortion, or obtain admitting privileges for their doctors at nearby hospitals. For example, in 2011, the U.S. Court of Appeals for the 5th Circuit upheld a Texas law requiring a woman seeking an abortion to see a sonogram of the fetus and hear its heartbeat before undergoing the procedure. Courts in Arizona and South Carolina have also upheld regulations targeting abortion facilities in the past.

Scott Gaylord, an associate professor at Elon University School of Law, said the legal cases that are being filed in response to this burst of activity are “extremely important because the legislatures are pushing in new directions, [and] states are handling these issues somewhat differently.”

How the courts end up ruling, he said, “really helps set the tone and will set important precedents.”

In at least three instances — Arizona, Georgia and Idaho — federal and state judges have struck down abortion bans at 20 weeks after fertilization as unconstitutional (the Arizona ban was set at 18 weeks). The bill passed in Texas contains a 20-week provision, but the legislation is structured so that even if that section is struck down, other parts of the bill could remain in effect.

Abortion rights groups have moved quickly to challenge a half-dozen laws this year. In Wisconsin, a federal judge issued a temporary restraining order against a law requiring every physician who performs an abortion at a clinic to have staff privileges at a local hospital. The ACLU and Planned Parenthood have sued, arguing that the measure would force two of the state’s four abortion clinics to close.

Judges in Alabama and Mississippi have blocked similar laws from taking effect by issuing injunctions. And in May, a judge temporarily halted an Arkansas law that would have prohibited abortions 12 weeks after fertilization.

The ACLU, the NAACP and the National Asian Pacific American Women’s Forum also filed suit in May against an Arizona law that bans abortion on the basis of gender and race selection, arguing that it is based on stereotypes about Asian Americans and African Americans.

Janet Crepps, senior counsel for the Center for Reproductive Rights, said some of the tighter rules on how abortion clinics operate have “been harder to challenge, though we’ve had some luck with the more extreme ones.” Last month in Kansas, for example, the center got a preliminary injunction blocking two provisions of a measure enacted this year that requires providers to endorse specific literature on abortion provided to patients and redefines what constitutes a medical emergency for a woman seeking an abortion.

In the case of the bill approved Saturday by the Texas legislature, Crepps added, “Taken together, it’s going to act like a ban, and what we hope is that if there’s a challenge the courts will see that these are the same as bans . . . and that they’ll strike them down.”

In North Dakota, Crepps’s group is challenging not only the law prohibiting abortions once there’s a detectable heartbeat, but also ones requiring abortion doctors to get admitting privileges at nearby hospitals, banning abortions for the sole purpose of sex selection and genetic abnormality, and outlawing non-surgical abortions using medication. A state judge has already indicated he will rule the medical abortion prohibition unconstitutional.

Maureen Ferguson, a senior policy adviser for the Catholic Association, said these efforts to block abortion restrictions defy the will of the public. A Gallup poll in December found that while 61 percent of respondents supported keeping abortions during the first trimester legal, 64 percent thought second-trimester abortions should be illegal, and 80 percent backed banning third-trimester abortions.

“No doubt the abortion industry will take this fight to the courts because they can’t win in the court of public opinion,” she said. “By a 2 to 1 margin, people support limits on late-term abortion and tighter oversight of the clinics that perform them.”

Abortion rights activists, for their part, launched a voter mobilization effort Saturday and pledged to punish politicians across the nation who voted for abortion restrictions. Richards sent an e-mail through Planned Parenthood Action Fund telling supporters they were “in it for the long run.”