In an interview with RAI state television, Renzi repeated a threat to veto the disbursement of European Union funds to countries that refuse to help Italy and Greece, who have taken in hundreds of thousands of migrants over the past three years.
"Italy cannot take another year like the one we've just had," Renzi said during the recording of a talk show. He said the flow of arrivals must be curbed by March, without saying what would happen if it was not limited.
From Friday until Sunday, Italy's coastguard coordinated more than 6,000 sea rescues, bringing arrivals so far this year to almost 155,000, which was the total for all of 2015. In 2014 there were 170,000 arrivals.
Another 500 people were rescued from four different boats on Tuesday, the coastguard said in a statement.
For a third year, people smugglers are taking advantage of chaos in Libya to send migrants fleeing violence and poverty in Africa and the Middle East on overcrowded boats toward Italy and the EU.
More than 3,100 have died or disappeared trying to cross the the Mediterranean from North Africa this year, the International Organization for Migration estimates.
The prime minister has frequently denounced a lack of European solidarity amid the migrant crisis as Italy seeks EU approval for an expansionary budget that includes some 3.9 billion euros ($4.25 billion) in spending on migrants next year.
Renzi sharply rebuffed European Commission criticism of his budget for raising previously agreed deficit and debt targets.
"Instead of opening their mouths, they should open their wallets," he said.