"After the first attack the system was immediately strengthened," said the source, who asked not to be named, after Britain's Guardian newspaper said the ministry had come under a sustained cyber offensive -- and officials suspected Russia.
Russia's foreign ministry said there were "no facts to prove this claim," according to Italian media reports.
The Italian source, who has close ties to the foreign ministry, said the attacks "did not affect the encrypted information system used to exchange the most sensitive information" but did affect "email accounts of ministry employees and the embassies".
Any sensitive information sent by email from the embassies would also have been protected because it would have been encrypted.
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The daily said the hack was being investigated by Rome's chief prosecutor.
There have been concerns in recent weeks that Moscow has stepped up a cyber campaign against several European countries including Germany, France, Norway and the Netherlands.
Russia's alleged interference in the US presidential campaign last year by reputed hacking of Democratic Party computers and leaks of embarrassing communications raised fears the country may try to interfere in upcoming European elections.