“There has to be a fixed number of arrivals. We should not feel guilty if we are not able to welcome everyone,” Renzi said in a video posted on his party's website.
“We have to save everyone, but we are not able to welcome everyone into Italy,” he said.
Italy has been struggling to cope with a flood of migrants, mostly sub-Saharan Africans, crossing the Mediterranean Sea from Libya, a journey that has so far claimed more than 2,200 lives this year, UN figures show.
According to the International Organization for Migration (IOM), the country has accepted around 85,000 of the 100,000 people who have arrived this year – an influx that has revived fears of a return to the European Union's migrant crisis of 2015, when hundreds of thousands of people arrived on the continent in search of a better life.
The massive wave has also exacerbated tensions with neighbouring Austria, which this week threatened to send troops to its border with Italy to stop migrants entering.
On Thursday, EU interior ministers backed an urgent European Commission plan to help crisis-hit Italy, which earmarks 35 million euros ($40 million) in aid for Rome as well as proposals for working with Libya and other countries to stem the flow of migrants.
The ex-Italian premier also warned that countries which fail to help with the migrant crisis “will suffer the consequences” in upcoming European Union budget negotiations.
“These countries that take Italy's money but build walls, if we become tougher and more determined in the discussions for the (EU) 2020-2026 budget in the coming months, they will suffer the consequences,” he said.
Government data released on Thursday showed that Italy has received 73,000 asylum applications since the start of the year – an increase of 46 percent compared with the first six months of 2016.