"The landings are non-stop and the emergency is increasingly glaring," Interior Minister Angelino Alfano told Rai Uno public radio.
"Right now two merchant ships are rescuing two boats with 300 and 361 people aboard. It appears there's at least one corpse on board," he said.
Alfano estimated that 15,000 migrants crossing the Mediterranean had been rescued so far this year and said up to 600,000 migrants from Africa and the Middle East were ready to set off from Libyan shores.
"Europe must take the situation in hand. It cannot say that, having given €80 million to Frontex, the problem has been resolved," he said, referring to the European Union's border control agency.
"There are death merchants who profit from this people trafficking and who send out requests for help just 30 to 40 miles after leaving the Libyan coasts," he said.
Italy reported a 60-percent increase in asylum claims last year - mainly people fleeing the war in Syria - although numbers of arrivals are still lower than in the wake of the Arab Spring revolts in 2011.
The latest increase comes just ahead of European Parliament elections next month and lawmakers from the anti-immigration Northern League - a small opposition party - were quick to weigh in on the issue.
Davide Caparini and Nicola Molteni released a statement urging Alfano to stop the arrivals "by turning them back" and complained that asylum-seekers receive better treatment "than any Italian citizen".
But Silvia Canciani, a spokeswoman for the Association for Legal Studies on Immigration (ASGI), played down the scale of the new influx.
"The number of people arriving is increasing but it is only becoming an emergency because of the bad management of Italy's asylum system," she said.
She said the new arrivals would likely be taken to private accommodation such as hotels "because there is no more space" in Italy's asylum and immigration centres, warning vulnerable migrants such as minors risked not receiving the care they needed.
"This is very similar to the North Africa emergency in 2011. The Italian government is repeating the same mistakes," she said.
The navy said it had rescued around 2,500 migrants of the 4,000 arrivals and that others were being intercepted by merchant ships and coast guard vessels.
"This is the highest number we have had over a 48-hour period since Mare Nostrum began," a navy spokesperson told AFP.
Italy began its naval operation "Mare Nostrum" ("Our Sea") - a Latin reference to the Mediterranean - after more than 400 migrants from Eritrea and Syria perished in twin tragedies off Italian shores in October 2013.
Five navy ships are currently operating in the region south of the tiny Italian island of Lampedusa, which has become one of the biggest gateways for irregular migration into the European Union.
The navy said it has fed and carried out health checks on board its ships for the new arrivals, who will be taken to the ports of Augusta and Pozzallo in Sicily later on Wednesday.
The navy also said it had begun identity checks with police on board. "Some have documents, others do not. We are still trying to ascertain the countries of origin," the spokesperson said.
But campaigners have criticised these types of checks, saying migrants may not be fully informed of their right to ask for asylum on board the navy vessels.
"The rules for identification at sea are not very clear. It should be done on land," Canciani said.