PHOENIX — Officials from 16 states are lining up behind Arizona’s bid to enforce its year-old ban on abortions at or after 20 weeks of pregnancy.

A legal brief filed this week at the U.S. Supreme Court by those states does not dispute the 2012 Arizona law would outlaw abortions prior to a fetus being viable outside the womb. That is generally considered about 23 or 24 weeks into pregnancy.

But Ohio State Solicitor Eric Murphy, writing on behalf of his state and 15 others, told the justices that Arizona lawmakers had a legitimate reason to enact the 20-week ban: to protect against fetal pain and promote maternal health.

But the key to whether the Supreme Court agrees to hear the case — and, ultimately, reverse a federal appellate court injunction against the law — is Murphy’s contention that the Arizona law does not impose a substantial obstacle to a woman obtaining an abortion.

That is crucial, because even supporters of the 20-week ban concede prior Supreme Court rulings have declared such restrictions unconstitutional.

The law makes it a crime for a doctor to perform an abortion if the probable gestational age of the fetus is “at least 20 weeks.” But Murphy said that still leaves Arizona women the right to obtain an elective abortion prior to that.

“Arizona’s law merely challenges elective abortions to the time before a fetus may suffer great pain and before the risks to the woman’s health are greatest,” Murphy wrote. But he said that still gives a woman adequate time to decide whether to have an abortion.

But Arizona, even with the support of the other states, has other potential legal obstacles in convincing the nation’s high court the appellate judges were off-base in voiding the Arizona law.

In their ruling, the appellate judges cited an earlier Supreme Court ruling that said “before viability, the state’s interests are not strong enough to support a prohibition of abortion or the imposition of a substantial obstacle to the woman’s effective rights to elect the procedure.”

Murphy, however, is urging the Supreme Court to focus on the word “prohibition.” He agreed that would make it illegal for Arizona to have a “complete ban” on a woman’s right to choose.

But Murphy argued that “narrower bans on certain pre-viability abortions” remain legal. And he said the Arizona law fits that category.

“Each pregnant woman in the state retains the ultimate choice,” he wrote. “The law merely requires women to make that choice in the first half of pregnancy, before unborn children can feel pain and before the risk of medical complications dramatically rises.”

Murphy said the Arizona law, and similar ones elsewhere, do not place an “undue burden” on a pregnant woman with a pre-viability fetus but “merely channel the woman’s choice rather than prohibit it.”

Murphy also argued to the high court that banning abortions at 20 weeks would affect a relatively small number of women, citing figures showing fewer than 2 percent of pregnancies in the state are terminated at or after that point.

The 9th Circuit, however, dismissed those data as irrelevant.

“A prohibition’s constitutionality is measured by its impact on those whom it affects, not by the number of people affected,” the judges wrote. “The proper focus of constitutional inquiry is the group for whom the law is a restriction, not the group for whom the law is irrelevant.”

The justices have not decided whether to even consider the bid to review the 9th Circuit ruling, much less overturn it. They gave the Center for Reproductive Rights, which sued on behalf of doctors opposed to the law, until the end of November to respond.