Sarah Shourd, Shane Bauer's mother, and Josh Fattal's mother and brother called Thursday for the U.N. special investigator on human rights in Iran to investigate the case and seek the men's immediate release.
Bauer, 29, and Fattal, 28, have been held in Iran nearly two years on espionage charges. A July 31 trial is set.
They deny the charges and say they thought they were hiking in a scenic area of northern Iraq near Iran's border.
Shourd, Bauer's fiance, was arrested at the same time and released last year on $500,000 bail.