More than 20 people are reported to have been killed after a barrage of rockets slammed into a former military base near Baghdad international airport that houses a group of Iranian exiles.

Officials said three Iraqi soldiers were killed, and Iranian exiles said at least 20 of their people died in the attack late on Thursday.

Iraqi police said 16 rockets hit Camp Liberty, a former US base that now houses the exiled Iranian opposition group known as the Mujahedin of Iran (MEK). They said at least 16 soldiers guarding the camp were also wounded while MEK said dozens of Iranian refugees were wounded as well.

No one immediately claimed responsibility for the attack.

The statement from MEK said that “due to darkness of the night, the exact number of dead and wounded has not been established”.

Police said that there may be casualties among the exiled group, but said numbers had not been reported to the local authorities so they could not determine how many civilians were hit in the attack.

The MEK statement on casualty figures could not be independently verified because of the late hour of the attack and the camp’s inaccessibility to media.

A police official added that the rockets landed far enough from the airport that they did not disrupt commercial traffic. A hospital official confirmed the casualty figures. Both officials spoke on condition of anonymity because they were not authorised to speak to the media.

This was not the first attack since Camp Liberty became home to the Iranian group, which is strongly opposed to Iran’s clerical regime. Last year, the Islamic State group was said to have fired rockets near to Baghdad International Airport as it attempted to destabilise the capital.

Maryam Rajavi, president-elect of the Paris-based National Council of Resistance of Iran, the parent organisation of MEK, blamed the attack on Iran.

“The Iranian regime’s agents within the Iraqi government are responsible for the latest assault,” she said in a statement. “The United States and the United Nations are fully aware of this reality.”

In Washington, US secretary of state John Kerry condemned the attack in statement issued on Thursday night.

“We are consulting with the government of Iraq to ascertain the full extent of this unprovoked attack,” the statement said.

“No matter the circumstances, on this point we remain absolute: the United States remains committed to assisting the UN high commissioner for refugees in the relocation of all Camp Hurriya [Liberty] residents to a permanent and safe location outside of Iraq.”

Members of the MEK were welcomed into Iraq by Saddam Hussein in the 1980s during the brutal war with neighbouring Iran. Their fortunes turned sharply with the Iraqi dictator’s toppling in the 2003 US-led invasion.

Iraq’s current Shiite-led Iraqi government, which has strengthened ties with Tehran, considers their presence in the country illegal.

The group regularly reports worsening health conditions within their isolated camp and accuses the Iraqi government of neglect and human rights abuses.