Leaders of the antiabortion movement said Thursday that they are in no hurry to overturn the landmark Roe v. Wade abortion rights decision, saying they plan to stick with their long-standing strategy of pushing for incremental restrictions despite the tantalizing prospect of a more conservative Supreme Court.

Even with Justice Anthony M. Kennedy’s announced retirement, these activists said they are not sure the time is ripe for a wholesale reconsideration of the 1973 ruling.

For decades, the movement has followed a methodical strategy of slowly chipping away at abortion rights, one state at a time, with measures that curtail the timing or nature of the procedure but steer clear of outright bans.

That playbook was warranted for two reasons, several of the activists said Thursday: They believed an outright ban would be struck down, and they weren’t sure the American public was ready for one.

Those realities are likely to remain true even if a more conservative jurist is confirmed to replace Kennedy — at least for a little while, several activists said.

“We’re certainly getting closer,” said Martin Cannon, an Iowa lawyer who is defending a new law there that bans abortions when a fetal heartbeat can be detected, at around six weeks. “But if you throw the Hail Mary pass and you pass a bill that gets too far ahead of your populace, I think it’s an unstable bill. There’d be a lot of celebrating, and rightfully so, but it might not last.”

News of Kennedy’s plans to retire sparked immediate jubilation — and fear — on the subject of abortion, one of the most divisive issues for the court and the nation. Kennedy has served as a pivotal vote on numerous issues before the court, and his record on abortion has been mixed. President Trump has vowed to nominate a conservative to replace ­Kennedy, and Senate Majority Leader Mitch McConnell (R-Ky.) has promised to push for a confirmation vote before the midterm elections in November.

Senators seen as potential swing votes in confirming President Trump’s next Supreme Court nominee weigh-in on their vetting process on June 28. (Jordan Frasier/The Washington Post)

Leaders of abortion rights groups said in a conference call with reporters Thursday that Roe is in such immediate peril that they were launching a massive, 50-state campaign to rally voters and pressure senators to vote against any nominee who would rule to overturn Roe.

“This is not a drill,” NARAL Pro-Choice America President ­Ilyse Hogue said. “The lawsuits necessary to overturn Roe or to criminalize abortion are moving through.”

Even if Roe were overturned, it would be left to the states to enact or alter their abortion laws — and to Congress, perhaps, to pass a federal ban or begin the process of floating a constitutional amendment.

And, first, a case must come before the court.

Several such cases are wending their way through lower courts, but it is unclear which of them, if any, could prompt the Supreme Court to reconsider Roe.

In Kentucky, abortion rights supporters are trying to block a law banning a procedure known as “dilation and evacuation,” often used in second-trimester abortions. In Mississippi, a law banning abortions after 15 weeks of pregnancy is under challenge. And in Iowa, Gov. Kim Reynolds (R) signed the law last month that bans abortions once a fetal heartbeat has been detected, usually around six weeks of pregnancy. That law — which abortion rights advocates say bars the procedure so early that it is equivalent to a ban — is also facing a court challenge.

Steven Aden, chief legal counsel for Americans United for Life, said he pines for the day when Roe v. Wade is overturned, and he believes that day is coming. But moving too quickly could bring unintended consequences, he said.

The Supreme Court has already declined to hear cases involving laws such as the heartbeat bill in Iowa, he noted.

The Kentucky bill may have a better shot of reaching the high court, he said, although there is no guarantee it will prompt a reconsideration of Roe.

Instead, Aden warned, it could face a fate similar to that of a case involving a set of abortion restrictions in Pennsylvania that went before the Supreme Court. In that 1992 case, Planned Parenthood v. Casey, the court upheld most of the restrictions — but in the process reaffirmed a woman’s constitutional right to an abortion.

It was one of the court’s 5-to-4 cases in which Kennedy cast the deciding vote.

“I understand the frustration that our friends in the pro-life movement feel when they say, ‘Well, I just want to end abortion,’ ” Aden said.

But when abortion restrictions aren’t upheld cleanly, he said, “I don’t think that’s good for the movement, and I don’t think it’s good for clarifying the rule of law on abortion. So we want to be wise and do as much as we can, as much as prudence allows and circumstances dictate.”

Cannon, the lawyer in the heartbeat case, believes it would make a good one to challenge Roe. But he also acknowledged the less-than-certain prospects for that, given that Planned Parenthood has sued to block the bill in state court.

He said the antiabortion movement has had the most success with laws that restrict procedures that are harder for the public to support.

“When the child is less developed, people aren’t as responsive to that,” he said.

The dilation and evacuation law, also known as the “dismemberment” law, is a good example of a measure that helps anti­abortion advocates make the case to people who might support some abortion rights, Aden said.

“Any law that helps people understand what abortion really is” has a better chance of surviving court challenge and also helps to move the dial on public opinion, he said.

Abortion rights advocates, meanwhile, challenged the notion that public opinion is moving against them.

Polls have shown that a majority of Americans want the next justice to uphold Roe. A CBS News poll in February found that 54 percent of those surveyed felt that way, while a 2016 Pew Research Center poll put the figure at 69 percent.

“We know that in all 50 states in this country, the majority of Americans do not want to punish women, believe in legal access to abortion, know what’s at stake and are ready to go out and fight this,” Hogue said. “It’s true in red states; it’s true in blue states.”

Rachel Sussman, national director of state policy and advocacy for the Planned Parenthood Federation of America, said Americans should expect a real challenge to Roe — and, in the wake of a high-court decision against the 1973 ruling, a rush by as many as 20 states to enact outright bans.

She also predicted more proposals at the state level to restrict access to abortion.

“Since 2011, we’ve seen over 400 restrictions enacted at the state level, all of them making it hard if not impossible to access abortion,” Sussman said.

“To me, not only is there a looming threat at the Supreme Court, but this is going to embolden states across the country.”

Paige Winfield Cunningham contributed to this report.