Marco Minniti, who meets his counterparts in Paris later Sunday to prepare for EU talks in Tallinn this week, said in an interview with Il Messaggero daily that "we are under enormous pressure".
With arrivals in Italy up nearly 19 per cent compared to the same period last year, Rome has threatened to close its ports to privately-funded aid boats or insist funding is cut off to EU countries which fail to help with the crisis.
"They are sailing under the flags of various European countries. If the only ports 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" that Europe wanted to help Rome, he said.
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Italy's Red Cross has warned the situation in the country's overcrowded reception centres is becoming critical.
Interior minister Minniti was set to meet counterparts Gerard Collomb of France, Thomas de Maiziere of Germany and European Union Commissioner for Refugees Dimitris Avramopoulos at 1800 GMT in the French capital.
The Italian minister said Rome would be pushing for a way to shift the asylum application process from Italy to Libya, and safely bring to Europe those who win the right to protection.
"And, on the basis of the decisions made by the UNHCR, we must ensure the former depart for Europe while economic migrants are voluntarily repatriated" to their countries of origin, 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".
Critics have said the NGOs attract traffickers by sailing close to the Libyan coast. The NGOs insist they have no choice, because smugglers put the migrants out to sea in flimsy vessels that sink as they reach international waters.
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