Renzi told a press conference after the figures were released by the International Organisation for Migration in Geneva that the numbers arriving from Libya so far this year were broadly in line with the 2015 pattern.
Fears are running high in Italy that the country could be confronted with a surge in migrants trying to reach its southern shores as a result of EU moves to close routes through the Greek Islands and the Balkans.
Italian officials are also wary of the possibility of neighbouring EU countries closing their borders, as France did temporarily last year and Austria is threatening to do now.
The interior ministry this week asked local authorities to find 15,000 extra beds to house asylum-seekers in anticipation of a possible increase in the numbers of people requiring accommodation.
"There is a problem that concerns our country but there is not an invasion underway," Renzi said.
"We have taken certain initiatives but we are not facing an invasion. It is a big problem but we have clear ideas about how to deal with it."
Renzi said the EU was working on deals with African countries to stem the flow of migrants leaving for Europe and to prevent those who do from being allowed to pass through transit countries.
"I do not want to play it down but I do want to send a reassuring message. The numbers of boats are barely a few higher compared to last year."
The IOM said that of the 6,021 migrants who have reached Europe by sea since Tuesday, only 174 had landed in Greece with the balance coming ashore in Italy.
IOM spokesman Joel Millman stressed there was no evidence yet to suggest the Italy arrivals were linked to an EU-Turkey deal which aimed at stemming the influx of people to the Greek islands.
Migrants who spoke to IOM staff in Italy all said they had crossed from Libya, most of them on rubber dinghies loaded with around 130 people.
"Many of them were from sub-Saharan Africa, and we have noticed an increase in numbers from the Horn of Africa, particularly Eritreans," Federico Soda, head of the IOM's Rome office, said in a statement.
"There have been very few Syrians leaving from Libya in recent months," Soda said.
Millman noted that with weather warming at the start of the main crossing season, Italy would likely see persistently high arrivals in the weeks ahead.
So far this year, more than 23,000 migrants have landed in Italy, compared to nearly 153,500 who have landed in Greece, the IOM said.