Tirana has offered to resettle some 210 members of the People's Muhajedeen of Iran, or Mujahedeen-e-Khalq (MEK) currently housed among about 3,000 people in Camp Liberty, near Baghdad.
State Department spokeswoman Jen Psaki said yesterday that the first 14 residents had left Wednesday "for permanent relocation in Albania."
"The United States expresses its appreciation to the government of Albania for its generous humanitarian gesture," she added in a statement.
But she also urged MEK leaders to "cooperate fully" with the relocation process being organized by the UN High Commissioner for Refugees and to help UN monitors have access to camp residents.
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A February mortar and rocket attack on Camp Liberty killed seven people, according to the group, and there has been deepening concern about the safety of the residents.
The MEK was founded in the 1960s to oppose the shah, and after the 1979 Islamic revolution that ousted him, the group took up arms against Iran's clerical rulers.
Then Iraqi leader Saddam Hussein allowed the MEK to establish a base called Camp Ashraf, northeast of Baghdad, after he launched the 1980-88 war with Iran.
The MEK says it has now laid down its arms and is working to overthrow the Islamic regime in Tehran by peaceful means. Britain struck the group off its terror list in June 2008, followed by the European Union in 2009 and the United States in September 2012.