Rescuers eventually had to go in through the roof to get to the children, and two firefighters died trying to save them.
"We tried our best, but when we got there, the children were trapped inside," a ministry official said. "We are very sorry for what happened. We tried as much as we could to save these people."
The fire broke about 11am on Monday local time, somewhere near the Gympanzee creche.
Authorities said emergency services arrived at the mall one minute after the fire was reported, but rescue efforts were hampered.
People inside the mall when the fire started spoke of the panic as crowds tried to escape, only to find some exits blocked.
Members of the public told Al Jazeera news there was no evidence of an organised evacuation plan.
One woman tweeted that she was left inside a changing room when staff left the store without telling her of the fire.
Another survivor, Hazel Amanda, an international teacher from Edinburgh in Scotland, told the BBC: "I was in Pizza Express in the mall ... with 17 children, aged three to four.
"The first we knew of the fire was when we saw the smoke. There were fire alarms going off in the building but they were barely audible. They were not sounding in the individual shops, they were so quiet. We were so lucky to be near the exit.
"The idea that the emergency services turned up a minute after the call about the fire was made is nonsense - they arrived after we were all safely outside and the fire was well under way."
The Villaggio Mall, which is about five years old, has a Venetian theme. Inside the building, narrow bridges run across a canal, and this appeared to further complicate escape for those inside.
In 2009 several people posted photos on the expatriate website Qatarliving.com of fire exit doors padlocked shut at Villaggio Mall.
New Zealand journalist Tarek Bazley was in the mall with his children.
"The first thing I heard of it was a very benign fire alarm - it sounded more like a doorbell - repeating in the background," he told Radio New Zealand.
After 15 minutes he asked an attendant whether he should be worried, but was told to "sit tight" and that it was usually a false alarm.
"About 10 minutes later, someone else, a member of the public, raced through this area and said, 'Everybody out, you've got to get out now. The other half of the mall is on fire.' That is what he said to me."
Bazley and his children left the building and could see an "extraordinary volume of black smoke coming out of the centre of this mall".
"It looked like you had 30 steam trains all pumping their smoke out above it."
Bazley said he wanted to leave the area as quickly as he could with his children, but was stopped from doing so.
"There was no access route on the road, it was absolutely rammed with people. A lot of rubberneckers on the road going past, and a complete lack of planning, a complete lack of co-ordination in terms of removing people from the area."
People from Spain, South Africa, Morocco and the Philippines were among the dead.
Qatar authorities last night said that public prosecutors had taken charge of the investigation, and that a broader investigation into safety requirements in buildings would be made.
