WASHINGTON — After Republicans lost the presidential election and seats in both the House and the Senate last year, many in the party offered a stern admonishment: If we want to broaden our appeal, steer clear of divisive social and cultural issues.

Yet after the high-profile murder trial of an abortion doctor in Philadelphia this spring, many Republicans in Washington and in state capitals across the country seem eager to reopen the emotional fight over a woman’s right to end a pregnancy. Their efforts will move to the forefront on Tuesday when House Republicans plan to bring to the floor a measure that would prohibit the procedure after 22 weeks of pregnancy — the most restrictive abortion bill to come to a vote in either chamber in a decade.

The bill stands no chance of becoming law, with Democrats in control of the Senate and the White House. Republican leaders acknowledge that its purpose is to satisfy vocal elements of their base who have renewed a push for greater restrictions on reproductive rights, even if those issues harmed the party’s reputation with women in 2012.

But beyond Washington, advocates on both sides of the issue say the chance to limit abortion in the near future is very real. Republican-dominated state legislatures in South Carolina and Wisconsin are weighing bans similar to the one the House will vote on, which would impose the 22-week limit based on the scientifically disputed theory that fetuses at that stage of development can feel pain.