That's according to a report released on Monday by the UN's Working Group on Arbitrary Detention on the detention of Siamak and Baquer Namazi.
The report comes as Iranian President Hassan Rouhani attends the world body's annual meeting in New York.
It puts new pressure on the moderate cleric's government to confront hard-liners within Iran's paramilitary Revolutionary Guard and judiciary. They repeatedly have arrested and prosecuted those with Western ties since the country's 2015 nuclear deal.
However, it remains unclear whether Rouhani has the power to free those detained. Analysts believe those held will be used by hard-liners as bargaining chips in future negotiations with the West.