Two-year-old Lillie, Jackson and Wilsher Weekes perished when a fire ripped through the daycare centre they attended in 2012. The centre was in a the Villagio Mall in Doha.
Last month a Qatari judge threw out the convictions of four people convicted of involuntary manslaughter and a public servant charged with forgery in relation to the blaze.
That ruling meant none of the five, who included the childcare co-owners, Villagio mall chairman and manager, will serve any jail time over the devastating fire.
Dr al Marri assigned prosecutors for the Court of Cassation prepare a document that outlines the reasons for the appeal verdict. He wants the document presented to him before it is filed in court.
Last month Jane and Martin Weekes, parents of the triplets, said they were devastated at the verdict.

