The helicopter ran into trouble amid heavy fog.
A 16-year-old was "assaulted" by morality police and has been in a coma since Sunday, activists say.
The execution has been widely condemned.
The UK Prime Minister called it "a callous and cowardly act carried out by a barbaric regime".
Ardern is the only current head of government listed as a signatory.
Topher Richwhite and Bridget Thackwray were jailed while on a world tour.
"No one has the right to accuse Iran in this regard."
State television reported 86 other people were injured.
Twenty-nine people died and more were injured when the bulding collapsed.
