The departure came three days after Italy said it could recall its top envoy for "urgent consultations" in wake of the Supreme Court refusing the pleas of the marines to spend Christmas back home.
A day after the order by the apex court, Italian Foreign Minister Paolo Gentiloni was quoted by the Italian news agency ANSA having told Parliamentarians in Rome that the ministry could recall Mancini but added that this did not mean Italy wish to cut diplomatic relations with New Delhi.
Meanwhile, Italian Defence Minister Roberta Pinotti had said in Rome that the full physical recovery of marine Latorre was "a priority for the government and nothing will be done to jeopardize his condition".
Pinotti added that Latorre, who was allowed to leave India in September for four months of medical treatment at home, is in no condition to travel.
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His leave was granted by the Indian government after he suffered a form of heart attack.
The two Italian marines, accused of killing two fishermen in Kerala in 2012, maintain that they fired on the two fishermen after mistaking them for pirates while guarding an Italian oil tanker.
The situation has led to tense relations between India and Italy, which says that India has no jurisdiction in the case.