"We are under enormous pressure," Marco Minniti, who meets his counterparts in Paris later on Sunday to prepare for EU talks in Tallinn this week, said in an interview with Il Messaggero.
With arrivals in Italy up nearly 19 percent over the same period last year, Rome has threatened to close its ports to privately-funded aid boats or insist that funding be cut to EU countries which fail to help.
"There are NGO ships, Sophia and Frontex boats, Italian coast guard vessels" saving migrants in the Mediterranean, Minniti said, referring to the aid boats as well as vessels deployed under EU border security missions.
"They are sailing under the flags of various European countries. If the only ports where refugees are taken to are Italian, something is not working. This is the heart of the question," he said.
"I am a europhile and I would be proud if even one vessel, instead of arriving in Italy, went to another European port. It would not resolve Italy's problem, but it would be an extraordinary signal" of support, he said.
More than 83,000 people rescued while attempting the perilous crossing from Libya have been brought to Italy so far this year, according to the UN, while more than 2,160 have died trying, the International Organization for Migration says.
Italy's Red Cross has warned the situation in the country's overcrowded reception centres is becoming critical.
"What is happening in front of our eyes in Italy is an unfolding tragedy," UN High Commissioner for Refugees Filippo Grandi said on Saturday.
One of the rescue organisations, SOS Mediterranee, which runs an aid vessel along with Doctors Without Borders (MSF), said forcing boats carrying migrants to go to other European ports would be logistically difficult.
If the order came, "we would have no choice, we would obey. But it would be completely impossible with more than 1,000 people on board," SOS Mediterranee spokeswoman Mathilde Auvillain told AFP.
"And then we'd need to make a stopover in an Italian port anyway to refuel, or we'd end up needing to be rescued ourselves."
After weeks or months spent in Libyan camps -- where many migrants are raped or tortured -- those rescued are already traumatised, "imagine adding two or three more days at sea. Our priority is to protect them," she said.
Minniti was to meet counterparts Gerard Collomb of France, Thomas de Maiziere of Germany and EU Commissioner for Refugees Dimitris Avramopoulos at 1800 GMT in the French capital.
Code of conduct
Minniti said Rome would be pushing for a way to shift the asylum application process from Italy to crisis-hit Libya, and safely bring to Europe those who win the right to protection.
"We have to distinguish before they set off (across the Mediterranean) between those who have a right to humanitarian protection and those who don't," he said.
Unsourced Italian media reports said Rome was likely to call for a European code of conduct to be drawn up for the privately-run aid boats, with the Corriere della Sera saying vessels that did not comply could be "seized".
Rome would like a regional maritime command centre to oversee all rescue operations from Greece to Libya to Spain, which would spread the migrant arrivals between European countries, it said.
And Italy insists that the EU refugee relocation programme -- which is largely limited to people from Eritrea and Syria -- should be expanded to include other nationalities, such as Nigerians, La Repubblica said.
Italy's influential Catholic community Sant'Egidio said an EU directive dating from 2001, drawn up to offer temporary protection to those displaced by the conflict in the former Yugoslavia, should be applied here.
"Isn't that the same situation we find ourselves in now in the Mediterranean?" said Sant'Egidio head Marco Impagliazzo.