The advice came a day after India's airports were put on alert to block any attempt by Italy's ambassador Daniele Mancini to leave the country.
"In connection with any protests, especially in Kerala state, related to the two sailors, citizens are urged to always maintain a vigilant and cautious attitude and stay away from any crowds," the Italian embassy in New Delhi said in a website advisory.
The warning reflected apparent Italian concern about a potential backlash after Rome refused to return the two marines charged with murdering two Indian fishermen off the southern state of Kerala last year.
Local media reported fishermen's groups in Kerala have staged protests against the decision not to return the sailors while state lawmakers have voiced outrage.
India's Supreme Court on Thursday said the Italian ambassador, who struck a deal for the marines to go back home to vote in last month's Italian election, should stay in the country until the next hearing about the dispute Monday.
Rome announced earlier in the week it was reneging on a commitment to send back the two sailors, Massimiliano Latorre and Salvatore Girone, to face trial.
Mancini had signed an affidavit giving his pledge the two would return. The dispute has been a major embarrassment for Indian Prime Minister Manmohan Singh, who has warned of "consequences" for ties if the pair do not return.
Singh's opponents have accused the government of incompetence for allowing the marines to go home while facing such serious charges, and the main opposition Bharatiya Janata Party has said Italy is treating India "like a banana republic".
The marines shot dead the fishermen, saying they mistook them for pirates Italy insists the marines should be prosecuted in their home country because the shootings involved an Italian-flagged vessel in international waters, but India says the killings took place in waters under its jurisdiction.
Ties between the two nations have also been soured by corruption charges over a $748-million deal for the purchase of 12 Italian helicopters that the Indian government now is threatening to scrap.
India's foreign ministry said Friday the "entire expanse of our interaction" with Italy was being reviewed while insisting Italy must "respect and abide" by the agreements between it and the Supreme Court.
In a snub to Rome, India has decided to downgrade ties and not to post to Italy its ambassador-designate who was due to take up his post next week.
While no commercial fallout from the dispute has yet been reported, both countries stand to lose if ties worsens sharply.
Earlier this month, before the dispute over the marines erupted, the Italian ambassador told local businessmen he hoped bilateral trade would double to $15 billion by 2015 from the current $8.5 billion.
The European Union has said it hopes "that a common solution can be reached through negotiation", the Press Trust of India reported.
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