The calls, only the third the families have received in more than 21 months, lasted less than five minutes, CNN reported.
Bauer, Fattal and Bauer's fiancee, Sarah Shourd, were arrested July 31, 2009, while hiking along an unmarked border between Iran and Iraqi Kurdistan, and accused of espionage. Iran freed Shourd last year, citing health reasons.
The men's trial was scheduled to begin this month but was delayed without an explanation.
The Bauer family in Minnesota and the Fattal family in Pennsylvania said the prisoners sounded "reasonably well" but had been on hunger strike for 17 days to protest their jailers' withholding their mail.
Their mothers, Cindy Hickey and Laura Fattal, said last week they were also fasting to protest their sons' treatment.
They said Monday they would keep up their "open-ended, rolling hunger strike" until their sons are freed.
"Their inhumane treatment has to end with their immediate release," a statement issued by the families read.
Celebrity Families of 2014 [PHOTOS]