Khobragade's lawyer, Daniel Arshack, said he didn't know what she would be doing at the UN mission, but "I fully expect her to stay in the US."
Khobragade has said US authorities subjected her to a strip-search, cavity search and DNA swabbing following her arrest.
Prime Minister Manmohan Singh has described her treatment as "deplorable."
In India, the fear of public humiliation resonates strongly, and heavy-handed treatment by the police is normally reserved for the poor. For an educated, middle-class woman to face public arrest and a strip-search is almost unimaginable, except in the most brutal crimes.
Harf, the department of state spokeswoman, said Kerry called India's national security adviser Shivshankar Menon, who has slammed the diplomat's treatment as "despicable and barbaric."
In an email published in Indian media on Wednesday, Khobragade said she was treated like a common criminal.
