Khurshid met the prime minister at his residence in New Delhi.
The PM had on Wednesday warned Italy of "consequences" for bilateral ties if it did not send back two marines facing trial in the country in the killing of two Indian fishermen.
In a strongly worded statement in both Houses of Parliament, where the government came under attack on the issue, Dr Singh had accused Italy of "violating every rule of diplomatic discourse" and termed as "unacceptable" its decision not to send back the accused marines Massimiliano Lattore and Salvatore Girone.
The two marines were permitted by the Supreme Court on February 22 to go to Italy for four weeks to cast their votes in general elections following a written assurance by Italian Ambassador Daniele Mancini that they will return by March 22. There are also demands that the Ambassador be expelled from the country.
The two marines are charged with homicide for killing two fishermen off the Kerala coast in February last year in an anti-piracy operation.
I won't leave India, says Italian envoy
'Does Italy rule over India or does an Italian?'
Don't link marines and Quattrocchi issues: Cong to BJP
Italy violated EVERY rule of diplomatic discourse: PM
Marines row: India toughens stand, may expel Italy envoy