ROME — Italy’s coast guard and navy as well as tugs and other commercial vessels joined forces to rescue migrants in at least 16 boats Sunday, saving hundreds of them and recovering 10 bodies off Libya’s coast, as smugglers took advantage of calm seas to send packed vessels across the Mediterranean.

The Italian Coast Guard said the bodies were found in three separate rescue operations off Libya’s coast. They were aided by a tug and a merchant ship in at least some of the rescue efforts. In one of those rescues, a cargo ship found three migrants dead and 105 survivors on a dinghy in the waters north of Tripoli.

In yet another dramatic rescue, migrants aboard a motorized rubber dinghy that was deflating were spotted by an Italian Navy helicopter. Boats in distress were being spotted so quickly Sunday that in one case, a navy vessel had just finished one rescue of 90 migrants when it immediately went to the aid of another migrant boat.

One rescue involved 311 people, including 16 children, saved from a fishing boat in the smugglers’ fleet.

Sunday’s drama at sea came a day after 3,690 migrants were saved from smugglers’ boats. Most of those migrants were still being taken to southern Italian ports even as the fresh rescues were happening.

The soaring numbers sparked the latest round of calls from far-right politicians in Europe for drastic action to stop migrants from reaching European shores, once and for all.

Far-right National Front leader Marine Le Pen said France should send migrants back across the Mediterranean.

A French patrol boat Saturday rescued 217 migrants from three rubber dinghies and detained two suspected smugglers before all were turned over to Italian authorities.

Criticizing European immigration policy, Le Pen said on Europe-1 radio Sunday that France should send migrants back to their port of departure so “traffickers know that no migrant will come ashore on our coasts.”

With Italy bearing the brunt of the arrivals for years now, the Italian far right, spearheaded by the anti-immigrant Northern League party, has also been pushing for a radical change in how the migrant sea arrivals are handled.

One such suggestion has been to keep rescued migrants aboard large ferries offshore until their asylum applications, a process that can take months or more, are examined. Then only those found eligible for asylum in Europe would come ashore.

Some of the migrants rescued earlier in the weekend were brought to tiny Lampedusa island, while others were headed to ports in Sicily or in Calabria, in the south of the Italian mainland, on Monday.

Temporary shelters for those rescued were running out of room for more even before this weekend’s new arrivals, local authorities had warned.