Kerry, who called up Menon, expressed regret over the arrest and strip-search of Khobragade in New York last week and said "this unfortunate public issue" should not hurt the "close and vital relationship" with India.
Khurshid also briefed Singh yesterday on the issue, the sources said.
The Prime Minister, who has been upset over the treatment meted out to Khobragade, has directed all concerned in the government to ensure "full resolution" of the issue, implying that the diplomat should be freed and the case against her withdrawn.
Singh had on Wednesday termed as "deplorable" the treatment that the 39-year-old diplomat had been subjected to.
The government had asserted in Parliament earlier that it will take strong steps to ensure the return of the diplomat and ensure restoration of her dignity.