The People's Mujahedeen Organisation of Iran, about 100 of whose members are living on the camp near the Iranian border, blamed security forces for the deaths of 23 residents, however.
Local hospitals did not report any casualties from the blasts, the causes of which were not immediately clear.
The explosions at Camp Ashraf follow two mortar attacks earlier this year on another camp housing the group, which is also known as the Mujahedeen-e-Khalq (MEK), in which at least eight people were killed.
"Not a single soldier entered Camp Ashraf," said Haqi al-Sharifi, the Iraqi official responsible for the camp.
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"There was no attack from outside against the camp, but what seems to have happened is some barrels of oil an gas inside Ashraf exploded. The police are investigating."
A police source told AFP, however, that five mortars landed in Ashraf today morning.
The MEK, meanwhile, said that the Iraqi army had entered Ashraf and killed 23 of its members and set fire to the group's property in the camp.
Former Iraqi dictator Saddam Hussein allowed the rebel MEK to set up the camp during the war with Iran in the 1980s.
Around 3,000 MEK members were moved from Ashraf to Camp Liberty, located on a former US military base on the outskirts of Baghdad, by September 2012, but about 100 stayed on at the old camp in order to deal with leftover property and goods.
"We deeply regret the tragic events of today, which have reportedly led to the killing and injuring of several camp residents," Eliana Nabaa, spokeswoman for the UN's mission in Iraq, told AFP.