Alfano was speaking at an event in Ostia, near Rome, in response to criticism from Monsignor Nunzio Galantino, the general secretary of the Italian Bishops Conference, of Italy's proposal to start fingerprinting migrants crossing the Mediterranean as soon as they are picked up by rescue boats.
The so-called ‘floating hotspots' “are a bad copy of detention centres”, Galantino told La Repubblica, adding that while on a ship, the right for migrants to seek asylum would not be ensured.
Italy and Greece have borne the brunt of Europe's refugee crisis, with 46,473 people landing on Italy's shores since the start of the year.
Some 13,000 were rescued by the Italian navy, coast guard and EU vessels in several shipwrecks last week, while at least 1,000 are feared dead.
A joint report published by Europol and Interpol last month said there were around 800,000 migrants in Libya waiting to attempt the journey across the Mediterranean.
Meanwhile, an EU plan devised last September to move 120,000 asylum seekers from Italy and Greece to elsewhere in the EU has fallen by the wayside.
“I understand Galantino's words, as a bishop, but I'm the interior minister and have a duty to ensure that laws are respect,” Alfano was quoted by Ansa as saying.
“We're the champions of the world when it comes to being humanitarian and welcoming. We have a big heart, but we can't welcome everyone.”
Galantino also said the migrant deaths were "a slap in the face to European democracy” and slammed the EU for failing to create “a humanitarian corridor, provided for by international law, towards countries willing to host migrants, in order to encourage safe passage and avoid violence, exploitation and deaths".