The navy has been picking up migrants in an operation called Mare Nostrum off the Libyan coast for a year.
But this year has seen a surge of migrant boats heading for Europe and at least 3,000 migrants have drowned.
A new EU operation, Triton, will have only a third of Mare Nostrum's budget, raising concern about future rescues.
Triton will focus on border control - tasks such as vetting asylum seekers once they are ashore, and coastal patrols - rather than search and rescue in international waters.
But Italy's Admiral Filippo Foffi told the BBC that EU-Italian naval co-operation must continue in international waters.
There has been no order to stop Mare Nostrum yet, Adm Foffi said. However, Italian officials have made it clear that they intend to scale down their operation, as the EU's Frontex border agency puts Triton into action.
Mare Nostrum was launched after hundreds of migrants drowned off the isle of Lampedusa, and was only intended to be a temporary mission.
So far EU countries have pledged to give Operation Triton six ships, two planes and one helicopter. Many more operational details are yet to be hammered out - including how much time they will spend in international waters.
"If we are only in territorial waters we won't see people in danger and if they die we won't see it," Adm Foffi warned.
He said he was waiting to see what resources Italy's EU partners would offer to Frontex, and stressed that Frontex was currently involved in search and rescue work, alongside the Italian navy.
Frontex "is not the owner of the capability" - it relies on member states offering personnel and equipment, he explained.
The UK has said it will not support future search and rescue operations to prevent migrants drowning in the Mediterranean.
Foreign Office minister Baroness Anelay said such operations could encourage more people to attempt to make the dangerous sea crossing to enter Europe.
There has been a rise in the number of migrants trying to reach Italy in the past year, with many setting sail from Libya packed into unseaworthy boats.
About 150,000 migrants - mostly fleeing violence in the Horn of Africa and Middle East - have been rescued by Italian ships over the past 12 months.
The Italian navy says it will continue search and rescue missions for migrants in the Mediterranean in parallel with an EU operation starting on Saturday.