BAGHDAD (AP) -- The first exiles from an Iranian opposition group have moved to Albania from a camp near Baghdad as part of a relocation process, the United Nations said Thursday, a step toward defusing an explosive dispute left over from the Iran-Iraq war of the 1980s and the U.S.-led ousting of the regime of Saddam Hussein.

In a statement, the U.N. envoy in Iraq, Martin Kobler, said 14 members of the Mujahedeen-e-Khalq arrived in Albania late Wednesday, the first of 210 set to travel to new homes in Albania.

The MEK, or the People's Mujahedeen of Iran, opposes Tehran's clerical regime. It carried out assassinations and bombings in Iran until renouncing violence in 2001. Several thousand of its members were given sanctuary in Iraq by dictator Saddam Hussein, who was deposed in 2003.

Since then, the MEK refugees have been a stubborn, anachronistic thorn in the side of Iraq and the United States, even after the U.S. turned over responsibility for Camp Ashraf, housing the remnants of the militant group, to the Iraqi government in 2009.

The MEK fought alongside Saddam's forces in the 1980s Iraq-Iran war, and its members fear persecution and death if they return to Iran.

The Shiite-led government in Baghdad that replaced Saddam's regime is bolstering its ties with Iran. It considers the MEK a terrorist group and wants its members out of the country.

The MEK exiles have come under fire from armed Iraqis who demand their expulsion. In one incident, seven people were killed in a rocket attack on the MEK camp in February. Later, the head of a Shiite militant group threatened to carry out more attacks on the camp if the MEK members refused to leave.

Last year about 3,000 MEK exiles were moved from their decades-long enclave in northeastern Iraq to a refugee camp outside Baghdad at a former U.S. military base, part of an effort to ensure their peaceful departure from Iraq. However, while Albania is taking in a small group, it remains unclear where the rest of the MEK members might go, leaving a clear potential for further violence.

The U.S. government praised Albania for accepting to host the MEK members, urging the Iranian opposition group to cooperate fully with the relocation process.

"The relocation of Camp Hurriya residents outside of Iraq is vital to their safety and security. It is the responsibility of the MEK leadership to facilitate for the residents of Camp Hurriya free and unfettered access to U.N. human rights monitors," said a statement by the U.S. State Department.

Albanian Interior Minister Flamur Noka pledged to quickly complete arrangements to resettle the 14. He told The Associated Press that they will get the refugee status immediately and then receive residence permits and proper documentation.

"They will be treated like every other Albanian citizen," he said, though "for the moment they will have the status of the refugee," meaning they will not be free to travel outside the country.

Then-U.S. Secretary of State Hillary Clinton negotiated the agreement with Albania and the U.N. to take in the 210 MEK exiles late last year.

The U.S. took the MEK off its list of terror groups in September 2012, raising a stiff protest from Iran, charging that the U.S. move was "a violation of America's legal and international obligations" that could threaten U.S. interests.

"There is much evidence of the group being involved in terrorist activities. Delisting it shows America's double standard policy on terrorism," Iran state TV said then. The U.S. distinguishes between "good and bad terrorists" and the MEK are now "good terrorists because the U.S. is using them against Iran," the TV report said.

The MEK spent large sums of money in years of lobbying for removal from the U.S. terror list, holding rallies in European capitals and elsewhere.

On Thursday, Kobler described the transfer of the first group as "an encouraging first step in the relocation of the group of 210 residents the Albanian government has agreed to receive."

Ortenc Balla, a U.N. official in Tirana, said the 14 were in an asylum-seekers center. "The Albanian government has undertaken all the responsibilities, including their security," he told the AP.

Phone calls to the Iraqi government and MEK officials went answered.

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Associated Press writers Llazar Semini in Tirana, Albania and Bradley Klapper in Washington contributed.