Sameer Sabir (34) and Nada Siddiqui (29) were being comforted by loved-ones today as fresh details emerged about the one-year-old's death.
The baby died from severe head injuries on January 16 after being allegedly battered two days earlier by Irish nanny, Aisling McCarthy Brady.
The Co Cavan woman, who cared for Rehma for six months, remained in a Boston jail today where she faces the prospect of a murder charge.
But breaking their silence on the tragedy, Rehma's parents appealed for privacy as they grieve the loss of their only child.
"The family of this child is going through unimaginable pain and suffering and their wellbeing remains a priority for us," a statement by the Middlesex district attorney said.
"Very few can fully understand the sorrow and pain that they are enduring, and we need to allow them the appropriate time and support they require to cope with this tragedy."
The baby's father, Sameer Sabir, is a British-born entrepreneur.
Her mother, Nada Siddiqui, is a Princeton-educated financial analyst who is originally from Pakistan. Ms McCarthy (34) is being held on $500,000 (¤375,000) cash bail as prosecutors continue to build their case against her. It's expected that she will face a murder charge when the official autopsy results have been studied. The nanny, who is originally from Moher, denies all charges against her.
The nanny -- who has lived illegally in the US for 10 years -- was in charge of the child on January 14 when she called emergency services.
Rehma had a broken leg and arm and was bleeding severely from her head and eyes when police found her that afternoon. She later died in hospital from serious swelling after doctors took her off life-support.
Ms McCarthy Brady married Cork painter Donald McCarthy in Boston in September and lives with him there.
Tanaiste Eamonn Gilmore confirmed that officials from the Department of Foreign Affairs have made consular assistance available to Ms McCarthy Brady.