Officials from the Council of the Islamic Revolution in Iraq (SCIRI) have blamed Friday morning's disaster on a bomb attack, but a senior US military officer said a structural defect was to the culprit.
The west Baghdad building, which also houses a religious school, collapsed on to families sleeping in the compound.
SCIRI spokesman Mohsin al-Hakim said an explosion had been detonated by remote control.
"We were asleep and suddenly about five o'clock in the morning (0200 GMT) the roof fell on us," said Ahmad Rahim, 23, a nephew of the woman who died.
Buried under rubble
"We were buried under the rubble and our neighbours came and helped us get out."
As he spoke, a shaikh from the religious school arrived and Rahim cried out: "Why didn't you tell us it is dangerous here?"
Sheikh Abd al-Wahid replied that bombings are happening all over Iraq. "It is Saddam's people who commit these attacks," he said.
US Brigadier General Mark Kimmitt, speaking at a press conference in Baghdad, said he had received a report indicating there was no explosion.
Ayat Allah Baqir al-Hakim was
assassinated in September
"The Iraqi police service reported to the 1st Armored Division that the building collapsed due to a structural integrity problem," he said.
SCIRI leader assassination
But Mohsen al-Hakim blamed "agents of the old regime and terrorists" for the incident, which came two days after a SCIRI member was gunned down outside his Baghdad home.
Muhammad al-Hakim was shot dead on Wednesday, Dr Hamid al-Bayati, the London representative for SCIRI, said.
"It's not the first time that our offices and officials have become victims of this kind of attack which aims to weaken us and remove us from the Iraqi scene," Mohsin al-Hakim said.
SCIRI was hit hard by the September car bomb assassination of Muhammad Baqir al-Hakim, its then leader. Another 82 people died in that attack in south-central holy city of Najaf.
Iraqi resistance fighters have launched a campaign of bombings and shootings against pro-US Iraqis, as well as US-led occupation forces, as they seek to end Iraq's occupation.