UN officials have criticised Operation Triton, the EU's new policy towards migrants trying to cross the Mediterranean from Africa to Europe.
Vincent Cochetel of the UN refugee agency said it put the onus on merchant ships to rescue those in trouble, but that ships might avoid responding.
A UN special envoy told the BBC it was outrageous that some states, including the UK, had opted out of Triton.
Triton is much smaller than the Italian mission it is replacing.
While the Italian mission, Mare Nostrum, conducted regular search-and-rescue operations, Triton will be focused on patrolling within 30 nautical miles of the Italian coast.
Mare Nostrum officially ended on 1 November, though the Italian navy is continuing scaled-back operations for about two months.
This year has seen a surge of migrants risking their lives to reach Italy. 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 big question mark is, now what's going to be the responsibility of private ship owners to rescue people in the high sea, because so far there was some sort of predictability with the rescue at sea on the Italian navy," Mr Cochetel told the BBC's Newsday programme.
The Italian navy "took the lead to save lives," he said. "Now that responsibility is going to be transferred to those private ship owners - will they switch on or switch off their signals when they get the call from the rescue centre in Rome?"
He cited an incident at the end of August in which there were 76 ships in the area of rescue.
"The call centre called them all, and within one minute there were only six ships left on the radar screen. All the others switched off their radar signal."
The UK has opted out of migrant rescues in the Mediterranean, saying such operations could encourage more people to risk dangerous voyages to Europe.
Peter Sutherland, the UN special envoy for migration, condemned such arguments.
"I think that it is an utterly outrageous statement to make that it is a good thing not to save lives because it may put other people off trying to travel across the Mediterranean," he said.
"I just find it incomprehensible that that argument could be considered to be morally justified."
The Italian navy has made it clear that, following international maritime law, it will still attend to an emergency or distress call from any boat, in any location.
But critics have warned that Triton's more limited resources may make it harder to rescue migrants in distress in international waters.
Operation Triton's budget, at 2.9m euros (£2.3m; $3.7m), will be a third of Mare Nostrum's. Run by the EU border agency Frontex, it will have six ships, four planes and a helicopter at its disposal, and a staff of 65.
The European Commission says 21 EU member states have pledged to participate.