The New Zealand parents of triplets killed in a mall fire in Doha hope that Prime Minister John Key's efforts on their behalf will result in the recall of two of those convicted of the deaths of their children from a plum diplomatic posting to Brussels.

Mr Key met with the Emir, Tamim bin Hamad Al Thani, while he was in Istanbul in the lead-up to the Anzac Day commemorations and said he raised concerns held by Jane and Martin Weekes with him.

"He absolutely assured me he wanted to see justice done, that he is personally following the situation and is committed to seeing justice completed for the family. I hope the Weekes family can take some heart from that," he said.

He said the Emir had told him he had personally met with the Weekes after the fire "and he remains utterly committed to making sure those who are responsible will be held to account".

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The Weekes' triplets, Lillie, Jackson and Willsher, were among 13 toddlers killed in the fire at the Villagio mall in 2012 while at daycare.

Five people were convicted of involuntary manslaughter for the 19 deaths on that day and all five had appealed. That included daycare owners, diplomat Sheikh Ali Bin Jassim Al-Thani and his wife Iman Al-Kuwari who were sentenced to six years in prison. Al Thani is serving as Qatar's ambassador to the European Union in Brussels while the appeal is underway.

Jane and Martin Weekes had asked Mr Key to convey their distress about that situation and were hopeful Mr Key had helped.

"We remain very distressed that two of the killers of our children are representing Qatar in Brussels and that they use that as an excuse not even to attend court. We hope they will soon be recalled."

They said they understood Al Thani was entitled to appeal the conviction but did not believe it was appropriate for a person in such a position to serve in a prestigious diplomatic posting while it was heard.

They said they were grateful to Mr Key for raising it with the Emir and looked forward to learning more of the Emir's response.