SACRAMENTO — The battle over abortion shifted to the states on Monday as a weekend of furious protest and prayerful thanksgiving in the wake of the Supreme Court’s Roe v. Wade reversal gave way to a coast-to-coast wave of lawsuits, legislation and pitched political fights.

With conservatives in roughly half of the states moving swiftly to end or dramatically restrict reproductive rights and liberals in roughly 20 more scrambling to preserve them, the national debate suddenly fragmented into a contentious patchwork, with lawyers and lawmakers arguing the fine points of state constitutions and statutes.

Abortion rights advocates in Kentucky, Louisiana, Texas, Idaho and Mississippi sued on Monday to halt or delay bans on abortion after Arizona advocates filed a similar court challenge over the weekend. In South Carolina, Planned Parenthood South Atlantic moved to withdraw a federal court challenge to a ban there, but apparently only so the organization could file a fresh challenge in state courts instead.

To understand why, one need only to look at Louisiana and Utah, where judges on Monday temporarily blocked enforcement of laws that would have banned abortion. Abortion rights advocates are coalescing around a strategy of asking courts for temporary injunctions that at the very least can buy time and allow abortions to proceed in the short term. One of Louisiana’s three clinics already said Monday that it would reopen.

“It’s all about the states from here on out,” Jessie Hill, a law professor at Case Western Reserve University who has worked on abortion rights cases, said. “We can fantasize about federal solutions to this issue or nationwide settlements of the abortion question, but I think that after Dobbs, I don’t see a lot of possibilities at the federal level.”

Ms. Hill is part of a team of lawyers challenging in federal court an Ohio law that bans abortions after about six weeks of pregnancy. A judge allowed that law to take effect after the Supreme Court ruling. But Ms. Hill added that she believes protections for individual rights in Ohio’s constitution could make for a compelling argument that abortion is protected in the state.

In Florida, providers on Monday deployed similar arguments in a court hearing, contending that privacy rights in the state’s constitution pre-empted a new state ban on the procedure after 15 weeks of pregnancy.

The Louisiana district court temporarily blocked “trigger” laws that would have criminalized nearly all abortions after health providers argued that the bans were unenforceable and vague and violated the state’s constitution. In Utah, the judge said he would temporarily block enforcement of an abortion ban in that state.

“There is irreparable harm that has been shown,” Judge Andrew Stone said. Lawyers for a clinic that sought the order said they had 28 women awaiting an abortion appointment on Monday. The temporary restraining order will be in effect for two weeks.

While the actions with the most immediate potential impacts occurred in states with bans or restrictions, states that support abortions moved swiftly Monday to shore up their protections as well.

In California, a supermajority of state lawmakers placed a constitutional amendment on the November ballot to explicitly protect abortion rights for that state’s 40 million people. In Washington, Gov. Jay Inslee said he would pursue a similar change in that state’s constitution to make abortion rights permanent in the aftermath of Friday’s watershed decision in Dobbs v. Jackson Women’s Health.

As states absorbed the end of a half-century old set of reproductive rights that had been guaranteed by the U.S. Constitution, the most striking impact was the swiftness with which it intensified already widening political fissures.

On Monday, attorneys general in 21 states and the District of Columbia issued a joint statement reassuring out-of-state patients that they would protect their access to abortion. The represented states included New Mexico, Minnesota and North Carolina, which could see more patients from nearby states with abortion bans.

That comes after attorneys general last week jointly asked the U.S. Department of Justice to protect anti-abortion organizations from violence. Among the states represented were Texas, Florida and Ohio.

In some places, state bans initiated by conservative lawmakers were challenged by more liberal cities. In Ohio, where courts permitted a 2019 law banning abortion at about six weeks to take effect after the Supreme Court ruling, Cincinnati’s mayor said Monday that he was taking steps to change the city’s health plan to reimburse city employees for abortion-related travel and for reproductive services to the extent they are allowed under state law.

“It is not my job to make it easier for the state legislature and governor to drag women back to the 50’s and strip their rights,” Mayor Aftab Pureval tweeted. “It’s my job to make that harder.”

In North Dakota, a fund-raising campaign raised more than a half-million dollars in three days to help move the state’s sole abortion clinic a few. miles to a new location on the other side of the Minnesota state line.

Several court challenges to abortion bans focused on state constitutions, particularly those in which a right to privacy is embedded. Alaska, Arizona, California, Florida, Hawaii, Illinois, Louisiana, Montana, New Hampshire, South Carolina and Washington all have specific provisions relating to a right to privacy.

Even in places where abortion rights supporters find relief in trial courts, they face a difficult long-term legal and political landscape. The state supreme courts in many places with restrictive abortion laws are dominated by justices who are Republicans or were appointed by Republicans. And even if certain abortion restrictions are deemed unenforceable, legislatures can try to pass new laws, and voters can seek to amend their state constitutions.

Joanna Grisinger, an associate professor of instruction at Northwestern’s Center for Legal Studies, said she also expects a number of abortion rights advocates to challenge the enforceability of “trigger laws,” which more than a dozen states enacted to quickly ban or restrict abortion after the Supreme Court decision.

“There’s all sorts of ways that a motivated state could probably try to continue, if they have the votes, to limit or ban most abortion access,” she said. “But there are certainly some strategies in the coming months we’re going to see pushing back against some of these.”

Ms. Grisinger predicted that there could be another round of court review if doctors are charged with crimes for performing abortions, believing that the mother’s health is at risk. Some abortion bans that provide exceptions for the life or health of the mother use relatively vague language that could put prosecutors and doctors at odds.

“I would at least anticipate challenges from doctors and medical associations as they really strive to figure out what they can do,” she said. But, she added, “a lot of this is going to wait until someone is prosecuted.”

Brigitte Amiri, a deputy director of the Reproductive Freedom Project at the American Civil Liberties Union, warned that court challenges, while important, were not a panacea for abortion rights supporters.

“Like we’ve often said, the courts are not going to be able to save us,” Ms. Amiri said. “That was true even when Roe was the law of the land — that you needed all the tools in the toolbox then. But I think even more so now. We have to diversify what we’re doing in terms of trying to ensure abortion access.”