Three New Zealand triplets were among 13 children who died when a fire broke into a shopping centre in Doha.
The two-year-old triplets were in a nursery in the Villaggio mall in Qatar's capital, Doha, when the fire started.
Radio New Zealand named them as Lillie, Jackson and Willsher Weekes.
New Zealand prime minister John Key offered his condolences. "It's a great tragedy," he said. "Their family are dealing with terrible grief. Obviously it's a very tragic day for that family."
Key said the children's grandparents were expected to fly to Qatar to be close to their children. New Zealand consular officials were offering assistance.
Speaking to Fairfax Media, Jo Turner, the children's grandmother, said: "Our daughter rang. What can you say? It's absolutely devastating.
"They were everything to her. She was a great mum. She was a hands-on mum."
Ms Turner said her daughter, Jane Weekes, had been living in Qatar for five years but had returned to New Zealand to give birth to the children.
Four Spanish children were also killed in the blaze, the Spanish foreign ministry said, but they were not named, and a three-year-old French child was also among the casualties.
Four teachers and two firefighters died, the Qatari ministry said on its official Twitter page.
Three nursery teachers who were from the Philippines died of smoke inhalation.
Authorities said another 17 people were injured including four children.
Thick black smoke could be seen pouring from the mall soon after the fire broke out. Smoke and flames hampered rescue efforts but the fire was extinguished within hours. Its cause has yet to be determined.
Qatar's interior affairs minister, Abdullah bin Nasser Al Thani, said: "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," he said in Doha.
Crown prince Sheikh Tamim bin Hamad al-Thani has ordered a special commission be set up to look into the fire, Al Jazeera reported.