Khobragade was arrested for allegedly underpaying her nanny and committing visa fraud to get her into the United States.
She was released after putting up a bail bond of USD 250,000, giving up her passport and pleading not guilty to the charges.
She faces a maximum of 15 years in jail if convicted on both counts.
The Indian housekeeper whose paycheck is at the centre of the dispute, Sangeeta Richard, is said to be upset and disappointed that the focus of the affair has shifted.
Meanwhile, Khurshid stated that the issue will be investigated and the U.S. authorities will handle the case.
"We have to believe that the two Indians, who are holding Indian passports, have conspired, and (that) there are some people who are a part of it. It has happened. Investigation will take place based on the arrangements in America about what exactly happened and who all were involved and the truth will come out soon. I hope that (the ) authorities in America will understand and handle the case with sensitivity and the big issues raised between us will be resolved soon," said Khurshid.
The U.S. Justice Department confirmed that Devyani Khobragade was strip-searched. A senior Indian government source has also said the interrogation included a cavity search.
However, a spokeswoman for the U.S. Marshals Service, Nikki Credic-Barrett, said Devyani Khobragade did not undergo a cavity search, but did undergo a strip search.
Under the agency's regulations governing prisoner searches, a strip search can include a "visual inspection" of body cavities, including the nose, mouth, genitals and anus, without intrusion.
Devyani told colleagues in an email of "repeated handcuffing, stripping and cavity searches, swabbing" and being detained in a holding cell with petty criminals, despite her "incessant assertions of immunity."
While common in the United States, jail strip searches have prompted legal challenges from civil liberties groups concerned that the practice is degrading and unnecessary.
An attorney with the American Civil Liberties Union, Ezekiel Edwards, said that despite a Supreme Court ruling last year upholding strip searches even in the absence of any suspicion that the individual has contraband or weapons, law enforcement authorities should make an effort to distinguish between prisoners who merit invasive searches and those who pose no risk.
The controversy over Khobragade's experience is not the first time that overseas observers have been horrified at the treatment of a foreign criminal defendant in the United States.
The Khobragade case is the latest concerning the Indian elite's alleged exploitation of their domestic workers, both at home and abroad.
Another official at India's consulate in New York was fined almost USD 1.5 million last year for using her maid as forced labour. Last month, the wife of a member of parliament was arrested in Delhi for allegedly beating her maid to death.
India says Khobragade's former housekeeper left her employer a few months ago and demanded help to obtain permanent resident status in the United States.
Under the Vienna Convention on Consular Relations, consular officials enjoy immunity from arrest only for crimes committed in connection with their work.
--ANI (Posted on 19-12-2013)