The dissident group Mujahadin-e-Khalq (MEK) said six people including a woman died after its camp was hit by mortars and missiles, while the UN mission in Iraq said it was aware of a number of deaths.
MEK calls for the overthrow of Iran's clerical leaders and fought alongside the forces of former Sunni dictator Saddam Hussein in the Iran-Iraq war in the 1980s.
It is now seeking to recast itself as an Iranian opposition force but is no longer welcome in Iraq under the Shi'ite Muslim-led government that came to power after U.S.-led forces invaded and toppled Saddam in 2003.
Iraqi Prime Minister Nuri al-Maliki is heavily reliant on Shi'ite Iran and leans on Tehran for political support at home and in the wider Sunni-dominated region, where he has few friends.
The attack struck the group's base in the former U.S. military compound "Camp Liberty" in the western part of the capital, where most of the group was relocated by Iraqi authorities last year from a base given to them by Saddam.
"At 5:30 a.m. around 18 Katyusha rockets landed in the camp, west of Baghdad, killing five people and wounding 42," said an Iraqi policeman at the base, speaking on condition of anonymity.
Another police source said between 25 and 45 people had been wounded.
Photographs and footage sent by the MEK to Reuters showed bloodied bodies laid out on blankets.
A spokesman for the group said they did not know for sure who was behind the attack, but said one likely suspect was Iran's Quds force - an elite unit of the Revolutionary Guards with a special focus on military operations outside the country.
MEK, which was formally removed from the U.S. State Department's official list of terrorist organizations last year, has blamed previous attacks on the Quds force.
Also known as the People's Mujahideen Organisation of Iran, the group led a guerrilla campaign against the U.S.-backed Shah of Iran during the 1970s that also included attacks on U.S. targets.
The United Nations intends to process them for refugee status in other countries, but they have complained that the conditions at Camp Liberty are poor and that they have not been permitted to bring many of their personal belongings.
Maryam Rajavi, who heads the Paris-based National Council of Resistance of Iran (NCRI), called on the UN High Commissioner for Refugees to speed up the process, asking the Iraqi government to return them to their former base "Camp Ashraf" in the meantime.
© Thomson Reuters 2013