* 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 context, related court case before justices, paragraphs 6-7, 16-17)
WASHINGTON, Jan 13 (Reuters) - The U.S. Supreme Court on Monday declined to hear Arizona's appeal of a lower-court ruling that declared unconstitutional a state law banning abortions beginning at 20 weeks of fetal gestation, meaning the restrictive measure is struck down.
The Arizona law, signed by Republican Governor Jan Brewer in 2012, had been considered one of the toughest in the United States in imposing limits on abortion.
A May 2013 ruling by the 9th U.S. Circuit Court of Appeals in San Francisco invalidated the law, saying it violated "unalterably clear" legal precedents. The high court justices' decision not to review the state's appeal means the lower-court ruling remains intact.
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 to impose limits on abortion.
The U.S. Supreme Court legalized abortion nationwide in 1973, but lawmakers in more conservative states in recent years have enacted laws that seek to place restrictions on the procedure, especially on late-term abortions.
These lawmakers have cited hotly debated medical research suggesting a fetus feels pain starting at 20 weeks of gestation. Lawyers for Arizona offered those arguments before the Supreme Court.
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 Arizona law was more restrictive than similar ones in other states because the way it measures gestation means it would bar abortions two weeks earlier than in other states that set the limit at 20 weeks.
Three abortion providers challenged the Arizona law in court. The appeals court had earlier blocked the law from taking 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 in a statement: "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.
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 Supreme Court justices, as is their custom, did not explain why they refused the Arizona appeal. The last time the high court took up an abortion case was 2007, when it ruled 5-4 to uphold a federal law banning a late-term abortion procedure.
The high court on Wednesday tackles a related matter when it hears arguments in a challenge by anti-abortion protesters to a Massachusetts law that seeks to ensure access for patients at clinics that offer abortions.
The law imposed a 35-foot (11-meter) zone at clinics that only patients, staff, passersby and emergency services are allowed to enter. The protesters said this violated their constitutional rights, including freedom of speech, by preventing them from standing on the sidewalk and speaking to people entering clinics.
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.
Arizona's 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 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 there are complications.