(CNN) -- The relocation of an Iranian exile group from a refugee camp in Iraq where they've lived for more than 25 years is nearing completion, the United Nations Assistance Mission for Iraq said Sunday.
The last major convoy of 680 members of the Mujahedin-e Khalq, or MEK, arrived at the new temporary site, a former U.S. military base near Baghdad International Airport, on Sunday, the United Nations Assistance Mission for Iraq said.
"This is an important step as we near the end of the relocation process," said Martin Kobler, special representative for Iraq of the U.N. secretary-general.
The U.N. is overseeing the process to find new homes for the 3,280 MEK members in third countries under an agreement reached with the Iraqi government last year.
"I urge the international community to speed up its efforts to accept residents in third countries," Kobler said.
MEK was placed on the U.S. terrorism list in1997 because of the killing of six Americans in Iran in the 1970s and an attempted attack against the Iranian mission to the United Nations in 1992. However, since 2004, the United States has considered the residents of Camp Ashraf "noncombatants" and "protected persons" under the Geneva Conventions.
Secretary of State Hillary Clinton is under a court order to decide by October 1 whether to remove MEK from the terror list. The secretary has said several times that her decision would be guided, in part, by whether the group moves peacefully from Camp Ashraf.
MEK leaders have been reluctant to complete the move from Camp Ashraf to Camp Hurriya, formerly an American facility known as Camp Liberty. They complained about conditions at the new camp, calling it more a prison than a home, after the first convoy arrived in February.
Camp Ashraf was established in 1986 after former Iraqi leader Saddam Hussein invited members of MEK to relocate to Iraq in an effort to undermine the Iranian government, which was then at war with Iraq. Iran also considers the group to be a terrorist organization.
A U.N. commission on refugees has described the residents as "formal asylum seekers" from persecution by the regime in Iran.
The arrival of the last convoy "marks a significant milestone in efforts to achieve a sustainable humanitarian solution to this issue," the U.S. State Department said Sunday.
A small group remains at the old camp to "residual issues and then also move to Camp Hurriya," the State Department said.
CNN's Mohammed Tawfeeq contributed to this report.