Mr Ban noted that many children are still being executed
UN Secretary General Ban Ki-moon has criticised Iran for what he says is an upsurge in executions in the country.
Iranian authorities say the executions are needed to fight drug trafficking.
Mr Ban welcomed a call from the head of Iran's judiciary to suspend the execution of children, but noted that the practice was still continuing.
The secretary general also used a new UN report on human rights in Iran to highlight the treatment of women, religious minorities and homosexuals.
Iran's deputy prosecutor general, Hossein Zebhi, has suggested that judges should stop imposing the death penalty on young offenders.
However on Monday, Mr Zebhi said that under Sharia law only a victim's family could commute a death sentence for murder.
At least six youths aged under 18 have been executed in Iran this year alone.
Praise and rebuke
The report on Iran also highlights moves against the women's rights movement.
It says women are repeatedly arrested for wearing headscarves that are too loose or coats that are too tight.
In addition, the document expresses concern about reports of violence against members of the Bahai community, a religious minority.
And it cites reports that homosexuals are routinely flogged and threatened with execution.
Mr Ban welcomed steps being considered by the Iranian parliament which would give women more legal rights, and called plans to establish children's courts a positive development.
He praised recent strides in education and health care.