At least 80 rockets struck Camp Liberty, where members of the main Iranian opposition group, the Mujahedin-e Khalq, or MEK, have been living since February 2012, said Shahin Gobadi, a spokesman for the People's Mojahedin Organization of Iran.
According to the group, the Thursday attack killed 23 residents of the camp and injured dozens more.
"This is a most deplorable act, and I am greatly concerned at the harm that has been inflicted on those living at Camp Liberty," said U.N. High Commissioner for Refugees António Guterres. "Every effort must continue to be made for the injured and to identify and bring to account those responsible."
About 2,200 people live at Camp Liberty, according to the U.N. refugee agency.
The U.S. State Department also weighed in on the attack.
"The United States strongly condemns today's brutal, senseless terrorist attack ... that killed and injured camp residents," U.S. Secretary of State John Kerry said in a statement
. "Our condolences go out to the families of the victims, and we hope for the swift recovery of those injured."
The exiled Iranian opposition group was moved to Camp Liberty more than three years ago
from another camp inside Iraq.
The camp was billed as a temporary facility at the time. A senior U.S. administration official said there were plans to keep it open until all of the camp residents were resettled outside Iraq.
Members of the Iranian opposition group have been housed in Iraq
for more than 25 years. Exiles, described as Iranian resistance figures and their sympathizers, live at Camp Liberty, also known as Camp Huriyya.
The MEK formerly was on the U.S. list of foreign terrorist organizations, 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, the State Department removed the MEK from the list in September 2012
, citing the group's renunciation of violence and the passage of a decade without its carrying out any attacks.
And since 2004, the United States has considered the residents of Camp Ashraf "noncombatants" and "protected persons" under the Geneva Conventions.
In the 1980s, then-Iraqi leader Saddam Hussein
invited members of the 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.
The current Iraqi government has closer ties to Tehran, and some opposition figures are afraid the camp will be subject to more attacks.