Four of the youngsters who died were Spanish, said a foreign ministry spokeswoman in Madrid, while Paris announced that a three-year-old French child also perished.
In Wellington, New Zealand Prime Minister John Key said the death of the triplets, believed to be three-year-olds, was "a great tragedy".
The children's grandparents were flying to Qatar to support the family and New Zealand consular officials were offering assistance, he added.
Radio New Zealand named the triplets as Lillie, Jackson and Willsher Weekes.
The blaze at the Villaggio mall left 19 dead in total, including 13 children -- seven girls and six boys -- and four female teachers, the Qatari interior ministry said on its Twitter account, citing the health minister.
Two civil defence personnel also died, it said.
Footage posted online showed black smoke billowing from the upmarket, Venice-themed complex as emergency vehicles rushed to the scene.
The fire broke out at a nursery, state minister for the interior Abdullah bin Nasser Al-Thani told reporters.
"The first report of fire at Villaggio was received by the operations centre at 11:02 am (0802 GMT)," he said, according to the QNA state news agency, adding that police and civil defence reached the site within minutes.
He said it became clear that 20 children were at the first-floor nursery and "all efforts were concentrated on evacuating those kids", adding firefighters had to break through the roof to gain access after a staircase collapsed.
Dense smoke inside the mall combined with the fierce temperature from the flames made reaching the trapped children very difficult, a civil defence representative told a news conference.
Expatriate New Zealand journalist Tarek Bazley said he was in the shopping centre with his two children when the fire broke out, but they escaped unharmed.
"The volume of smoke coming out of it, it looked like you had 30 steam trains all pumping their smoke out above it," Bazley told Radio New Zealand.
But he said there was a lack of urgency from officials in the mall when alarms went off and complained of a "complete lack of planning, a complete lack of coordination in terms of removing people from this area".
"The first thing I heard of it was a very benign fire alarm, it sounded more like a door bell to be honest," he said.
Health Minister Khaled al-Qahtani said all the fatalities were caused by asphyxiation, adding that 17 people were injured, mostly firefighters.
Crown Prince Sheikh Tamim bin Hamad al-Thani ordered a special commission set up to probe the deadly blaze, the Doha-based Al-Jazeera satellite television station reported.
In Madrid, a foreign ministry spokeswoman said: "Four of the dead children are Spanish," adding that Spanish embassy officials were trying to get more details.
Yamina Benguigui, the minister in charge of French expatriates, announced in Paris that a French child died, but declined to give any further details, including whether the victim was a boy or a girl.
"It is with great sorrow that I confirm that a French child aged three is among the victims," she said in a statement.
Villaggio Mall was opened in 2006, boasting a mall area of 125,000 square metres and featuring a canal on which genuine gondolas ferry visitors.
Thanks to its oil and natural gas wealth and a population of less than two million people, mostly foreigners, Qatar is one of the world's richest countries in income per capita terms, coming second only to tiny Liechtenstein.