WASHINGTON (Reuters) - President Barack Obama on Friday lifted restrictions on U.S. government funding for groups that provide abortion services or counseling abroad, reversing a policy of his Republican predecessor George W. Bush, a spokesman said.

The Democratic president’s decision was a victory for advocates of abortion rights on an issue that in recent years has become a tit-for-tat policy change each time the White House shifts from one party to the other.

When the ban was in place, no U.S. government funding for family planning services could be given to clinics or groups that offer abortion services or counseling in other countries even if the funds for those activities come from non-U.S. government sources.

Obama signed an executive order lifting the restrictions on Friday, a White House spokesman said.

It has been called the Mexico City Policy because it was unveiled at a United Nations conference there in 1984 and became one of the centerpiece social policies of the conservative administration of former President Ronald Reagan, a Republican.

Critics call it the “gag rule” because it also cuts funds to groups that advocate or lobby for the lifting of abortion restrictions, so they say it infringes on free speech. They also say it has reduced healthcare for some of the world’s poorest women.

Former President Bill Clinton, a Democrat, rescinded the rule when he took office in January 1993 and his successor, Republican George W. Bush, reinstated it in January 2001.

Planned Parenthood, a health care provider and advocacy group for abortion rights, welcomed the move.

“With the stroke of a pen, President Obama has lifted the stranglehold on women’s health across the globe,” Cecile Richards, the group’s president, said in a statement.

“No longer will health care providers be forced to choose between receiving family planning funding and restricting the health care services they provide to women.”

CRITICS ON BOTH SIDES

When he reinstated the policy after the Clinton administration, Bush said taxpayer funds should not be used to pay for or advocate abortions.

Anti-abortion activists agreed with Bush and criticized the move to lift the ban on funding.

President Barack Obama signs an executive order concerning the U.S. military base in Guantanamo in the Oval Office, January 22, 2009. REUTERS/Larry Downing

“When we wake up every morning to a deepening financial crisis, it is an insult to the American people to bail out the abortion industry,” said Charmaine Yoest, president of Americans United for Life.

“Planned Parenthood is a billion-dollar company and they do not need additional resources to burden the American taxpayer,” she added.

U.S. Senate Republican Leader Mitch McConnell also expressed disapproval. “I have long supported the Mexico City Policy and believe this administration’s decision to be counter to our nation’s interests,” he said in a statement.

The United States spends more than $400 million on overseas family planning assistance each year.

Critics of the funding ban say the anti-abortion restrictions have resulted in huge drops for funding worldwide to organizations that provide family-planning services and basic healthcare. They say this means many women are deprived of contraception and other health services in poor countries, leading to back-alley abortions and deaths.

The Center for Reproductive Rights says, for example, that in Ethiopia and Lesotho, some nongovernmental organizations are no longer able to offer comprehensive and integrated healthcare services to patients suffering from HIV/AIDS.

Abortion rights opponents and groups who support the Mexico City Policy dispute the view that it has led to an increase of illegal abortions or deaths overseas.

Unlike Clinton and Bush, Obama did not act on the rule on the January 22 anniversary of Roe v. Wade, the landmark 1973 Supreme Court ruling that made abortions legal throughout the United States.