* Last time Supreme Court heard abortion case was 2007
* Arizona faults "clear infringement" on state authority
* Abortion rights activists laud Supreme Court's refusal (Adds reaction from governor, abortion rights activists, paragraphs 4-5, 9-12, 17-18)
By Lawrence Hurley
WASHINGTON, Jan 13 (Reuters) - The U.S. Supreme Court on Monday declined to hear an appeals court ruling that said an Arizona law banning abortions starting at 20 weeks of gestation is unconstitutional, meaning the restrictive state law is struck down.
A ruling by the 9th U.S. Circuit Court of Appeals in May 2013 invalidated the law, saying it violated "unalterably clear" legal precedents. The justices' decision not to review the state's appeal means the lower-court ruling remains intact.
Arizona Governor Jan Brewer, a Republican, signed the measure into law in April 2012.
Brewer's spokesman, Andrew Wilder, said the Supreme Court was wrong not to hear the state's appeal, saying the action was "a clear infringement on the authority of states to implement critical life-affirming laws."
Abortion rights activists praised the Supreme Court's action, but expressed alarm at efforts at the state level in the United States to pass laws restricting abortions.
The Arizona law prohibited physicians from performing abortions starting at 20 weeks of pregnancy, except in medical emergencies, and could send doctors who perform them to jail.
Abortion rights groups said the measure was more restrictive than similar laws in other states because the way Arizona measures gestation means it would bar abortions two weeks earlier than in other states.
Those states also set the limit at 20 weeks but have different ways of calculating gestation time. Three abortion providers challenged the Arizona law in court. The appeals court had earlier blocked the law from going into effect, pending the legal challenge.
Wilder said Brewer was seeking to make Arizona "one of the most pro-life states," adding: "Governor Brewer will continue to fight to protect Arizona women, families and our most vulnerable population: unborn children."
The president of Planned Parenthood Federation of America, Cecile Richards, said, "A dangerous and blatantly unconstitutional law like Arizona's abortion ban should have never passed in the first place.
"Today, the court did the right thing, but women's health is still on the docket - not only at the Supreme Court, but in active cases all across the country," Richards added in a statement.
Nancy Northup, head of the Center for Reproductive Rights, said women's rights must not be "legislated away by politicians who are hell-bent on restricting access to the full range of reproductive health care."
The last time the Supreme Court took up an abortion case was in 2007 when it ruled 5-4 to uphold a federal law that banned a late-term abortion procedure.
In the landmark Roe v. Wade case in 1973, the court said that women have a right to have an abortion up until the time when the fetus becomes viable.
In a 1992 ruling, Planned Parenthood v. Casey, the court clarified that an abortion regulation can be legal as long as it does not impose an "undue burden" on women seeking the procedure.
The Arizona law bans abortions up to a month before the point of viability, which medical experts say is around the 23-to-24-week mark. The state already has a separate law banning abortions after a fetus is viable except when the mother's life is in danger.
Maricopa County Attorney Bill Montgomery, who argued on behalf of the law before the lower courts, called the Supreme Court's refusal to hear the state's appeal disappointing.
"Nevertheless, safeguarding the health and welfare of mothers and defending the dignity of life at all stages is a just cause and a duty of government. Today's decision does not relieve government of that duty," Montgomery said.
Several states, including Texas, have recently enacted laws restricting abortions. One of the provisions of the Texas law, which has also been challenged, requires doctors to have admitting privileges at a hospital within 30 miles (48 km) of the clinic where the abortion is performed in case women have complications.
The Arizona case is Horne v. Isaacson, U.S. Supreme Court, 13-402. (Additional reporting by David Schwartz in Phoenix; Editing by Will Dunham and Jonathan Oatis)