In an address to mark International Holocaust Remembrance Day, Napolitano said the threats were "a miserable provocation against all of us".
Those behind the threats "have nothing to do with Rome and Romans, who, out of human and civilized sentiment, democratic awareness, education and culture, stand in brotherly solidarity beside men and women of Jewish origin and religion," Napolitano said.
Police are probing three parcels containing pig heads were sent last to the Israeli embassy in Rome, the town's main synagogue and to a museum holding an exhibition on Jewish culture.
The threats drew criticism from the Israeli government and representatives of Italy's Jewish communities as well as Rome's mayor Ignazio Marino and other politicians including integration minister Cecile Kyenge.
Far-right groups are suspected of being behind the threats which prompted authorities to boost security in Rome in key areas including the synagogue on Monday, when events marking Holocaust Remembrance Day were taking place.
Police arrested two men on Monday who admitted scrawling xenophobic and anti-Semitic graffiti on building near Rome's criminal courthouse signed 'Militia'.
One of the two men arrested was investigated last year as part of a fresh probe into Italian branch of the neonazi Stormfront, an international body founded by Don Black, the former head of the US white supremacist movement the Ku Klux Klan.
Four men were in April last year convicted of inciting racial hatred on a neonazi website and sentenced them to between two and three years of house arrest, following an earlier probe of Stormfont.
The four men from central and northern Italy were found guilty of targeting "Jews and immigrants, advocating the supremacy of the white race and instigating racism and Holocaust-denial".