The fire in the 10-story building, which had only one exit and latticed balconies, started Tuesday evening when residents fell asleep.
Neighbors and residents of the building in the south-west of the capital said they heard screams as people struggled to escape the flames and thick smoke.
Police said 56 people were killed and 37 injured, while state media reported three children were among the dead.
At the mortuary of a military hospital, officials appeared at the entrance every half hour to announce over a loudspeaker that there was another victim for families to identify.
Holding up a photo on a cell phone or simply describing the dead, medical workers asked desperate relatives if they recognized their loved ones.
Every time a match was found, cries broke out.
Authorities tried to prevent families from speaking to journalists, but one man, who did not give his name, said his daughter had died and feared his wife had also died.
“I lost my daughter, who was staying with her mother,” he said through tears.
He was unsure where his wife was and told AFP: “I don’t think she made it either.”
A group of five women sitting on the ground outside the morgue said their “entire family had disappeared”.
“They were our children and grandchildren,” they said.
‘So much suffering’
Elsewhere at the mortuary, families who knew their loved ones had died waited for hours to retrieve the bodies.
One man, who gave his name as Dung, said his two young cousins, a man and a woman, were among the dead. They had come from their home in the nearby coastal province of Thai Binh to study.
‘They went to university here. Our family bought this small apartment for them.
“We are waiting here to take them back to our home province for burial, but we don’t know when they are going to release the body.”
State media reported that Hanoi would provide about $1,500 to families for each adult who died. Compensation would also be given to those who had lost a child.
The apartment complex, located in a narrow alley in a residential area of the capital, was home to several young families. Many had come from other provinces to work or study.
About 150 people lived in the building, which had no emergency ladder on the outside.
Survivor Tran Thi Lien, 65, who bought her second-floor apartment in the block eight years ago, told AFP that residents had often asked for better fire safety equipment.
“They still haven’t done it,” she said.
“When people die like this… it causes so much suffering.”
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