"A regret for the sake of formality is not enough. They should apologise in unambiguous terms and accept their mistake," he told reporters here.
Nath said all countries should draw a lesson from the incident and "raise their voice" whenever such a thing takes place.
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Prime Minister Manmohan Singh had yesterday described as "deplorable" the way the diplomat was treated in the US.
There is a strong demand that Khobragade be released unconditionally and all the charges against her dropped.
The government has taken a strong view of the diplomat's ill-treatment and announced a series of steps to strip US diplomats and their families of privileges, including withdrawing all airport passes and stopping import clearances for the Embassy, including for liquor.
39-year-old Khobragade, a 1999-batch IFS officer, was taken into custody last week on a street in New York as she was dropping her daughter to school and handcuffed in public on visa fraud charges before being released on a USD 250,000 bond after pleading not guilty in court.
She has been transferred to the Indian Mission to the UN to give her fuller diplomatic immunity.