At least some of the victims died as rescuers struggled to reach a child care center at the Villaggio mall in the capital Doha, according to Qatar's Minister of State for Interior Affairs, Sheik Abdullah bin Nasser Al Thani.
"We tried our best, but when we got there, the children were trapped inside. We are very sorry for what happened. We tried as much as we could to save these people," Sheik Abdullah told reporters in Doha.
Four of the children killed were Spanish citizens living in the small Arab emirate, the Spanish Foreign Ministry said. It did not identify the children, citing Spanish privacy regulations.
Also, a 3-year-old French child was among the victims, the deputy minister for overseas French citizens, Yamina Benguigui, said in a statement.
Two-year-old New Zealand triplets, Lillie, Jackson and Willsher Weekes, were among the victims, according to New Zealand media reports.
"Our daughter rang. What can you say? It's absolutely devastating," the children's grandmother, Jo Turner, told Fairfax Media. "They were everything to her. She was a great mum. She was a hands-on mum."
Turner said her daughter, Jane Weekes, had lived in Qatar for about five years, although she had returned to New Zealand to give birth to the triplets. The triplets' father, Martin Weekes, is listed on his LinkedIn networking site as a senior adviser at Qatar Media Services and a former chief executive of Auckland's Eden Park sports stadium.
Four teachers and two civil defense officials were among the dead, the Qatari ministry said on its official Twitter page.
At least three of the nursery teachers were from the Philippines and died of smoke inhalation, Philippine Foreign Affairs spokesman Raul Hernandez said in Manila.
Another 17 people were injured, including four children, according to authorities. Most of those hurt were rescuers responding to the blaze. A brother of one of the dead Filipino teachers was among the injured but had recovered, Hernandez said.
Witnesses earlier reported thick black smoke pouring from the ritzy mall around midday. Amateur photos and videos posted online showed firefighters rescuing victims by climbing on the roof.
The Interior Ministry said the fire was extinguished hours later.
The cause of the fire is under investigation.
Thick smoke and heat hindered rescue efforts, as did a lack of floor plans and malfunctioning sprinkler systems, the ministry said on Twitter.
Sheik Abdullah said all buildings in the country abide by safety requirements, but a special committee will nonetheless be set up to monitor building safety standards.
The Villaggio opened in 2006 and is one of Qatar's most popular shopping and amusement destinations. Retailers include many well-known Western brands, such as Foot Locker, Pizza Hut, Starbucks and British department store Marks & Spencer, according to the mall's website.
Malls throughout the oil-rich Arab Gulf are popular with families looking for entertainment destinations that provide relief from soaring summer temperatures. The Villaggio includes an ice skating rink, theme park, movie theater and indoor Venice-style gondola rides.
New construction projects such as the Villaggio have transformed the face of once-sleepy Doha in recent years, as the country benefits from a hydrocarbon boom. The OPEC member state is the world's largest exporter of liquefied natural gas.
Qatar won the right to host soccer's 2022 World Cup a year and a half ago.
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Associated Press writers Adam Schreck in Dubai, United Arab Emirates, Jorge Sainz in Madrid, and Nick Perry in Wellington, New Zealand, contributed to this report.
