Jane and Martin Weekes, the New Zealand parents of the triplets who died in last week's Villaggio Mall fire in Qatar, want outside experts brought in to help investigate the blaze.
The Qatar government should "seek the support from international fire and emergency experts to work alongside the team here to gather the facts", they said in a letter.
Their two-year-old triplets, Lillie, Jackson and Willsher, along with 10 other children, four teachers and two firefighters, were killed when the fire broke out at Villaggio, the country's largest mall.
The victims became trapped in a child-care facility as smoke from the fire spread.
Firefighters had to break a hole in the roof of the mall to reach the victims.
Abdullah bin Nasser bin Khalifa Al Thani, the country's minister of state for internal affairs, said at a news conference last week that the investigation would be handled internally.
The fire has raised questions about public safety in the Gulf emirate, the richest country per capita in the world with a population that has more than doubled in the past decade.
Qatar's public prosecutor ordered the detention of five people, including the mall's owner, manager and the owner of the child-care centre.
The six-year-old Villaggio mall is designed to resemble an Italian village, complete with canals and gondolas as well as an amusement park, ice rink and cinema.
The daycare facility was located in the middle of the mall, accessed through two narrow and winding hallways and up a flight stairs.
Qatari investigators are examining possible design flaws that funnelled dense smoke into areas around the child-care centre. Officials are also studying malfunctions in the sprinkler system and possible shortcomings in other safety measures, including alarms.
The findings from the investigation are expected next week.
* Bloomberg News with additional reporting by Associated Press