Pacifici was speaking during an event on Wednesday to mark the 70th anniversary since Jews in Rome were rounded up and sent to concentration camps.
He said that in Italy, a country of 60 million people, "there is room for everyone".
"60 million citizens can accommodate a few thousand people," he added.
Pacifici said that insitutions dealing with migrant arrivals in Italy need to be helped.
"We must ask them what we can do to help integrate and to see the children of migrants playing alongside ours."
More than 300 people from Eritrea and Somalia died when the boat caught fire and sunk off the coast of Lampedusa on October 3rd, while 155 survived.
Save the Children estimates nearly 22,000 migrants have arrived on the coasts of Sicily, Calabria and Puglia during 2013 – and 4,000 of them were children, many unaccompanied.