A total of 31 people died and another 40 are missing as sailors from the North African nation arrived to aid a pair of capsized boats.
Those who died included three children and 18 women.
The navy said many of the bodies recovered from the sea had bite marks and blue sharks were seen circling nearby as rescuers arrived on the scene.
A sailor who took part in the rescue said it was possible some of those who were missing had been eaten by the sharks, which can grow up to 12ft (3.8m) long.
A post on the Libyan Navy Facebook page described how the desperate survivors were clambering to stay on top of the overturned boats when they arrived on the scene.
vCard.red is a free platform for creating a mobile-friendly digital business cards. You can easily create a vCard and generate a QR code for it, allowing others to scan and save your contact details instantly.
The platform allows you to display contact information, social media links, services, and products all in one shareable link. Optional features include appointment scheduling, WhatsApp-based storefronts, media galleries, and custom design options.
The post said: “We found dozens of bodies floating in the water and two small boats with hundreds of people crowded on board and others holding on or trying to climb aboard to escape from the sharks.”
One sailor told Italian newspaper Il Giorno: “There were lots of bodies all around and we saw there were four or five sharks swimming among them, large blue sharks, a very aggressive species.
“When we brought the bodies on board we noticed that some of them had been bitten, so it’s possible that among the missing some may have been eaten.”
Officials said 200 migrants managed to survive the terrifying ordeal.
It is believed they were headed towards southern Italy or Malta, but their boats ran in to difficulty just 40 miles off the North African coast.
More than 160,000 people have crossed the Mediterranean en-route to Europe so far this year.
And nearly 3,000 are known to have died on the perilous route across the sea.
Migrant boats are often small, overcrowded and unsuited for the long journey.
The vessels are often operated by unscrupulous people traffickers who give little or no regard to the safety of their passengers once they have paid their fare and departed North Africa.
Around 1,800 people were rescued in the Mediterranean over a period of just four days last week.