At least 30 migrants are missing following two shipwrecks off the Italian island of Lampedusa, according to survivor testimony, as rescuers on Sunday winched to safety 34 others stranded on the rocks by rough seas.

Around 28 people were reported lost at sea by survivors on one boat, while three were reported missing from the second, after both went down in stormy weather on Saturday, said the International Organization for Migration (IOM).

Both were rickety iron boats believed to have set off from Sfax in Tunisia on Thursday.

Italy's coastguard said it had saved 57 survivors from the two shipwrecks, and recovered the body of a woman and a child.

It released dramatic footage Sunday of the rescues, in which people could be seen carried high on the crests of vast waves, while a coastguard vessel soared and plunged nearby.

While some people tried to climb onto the vessel as it rocked, others, wearing black rubber rings, clung desperately to one another in a human chain.

Cultural mediators with the IOM believed there were "at least 30 people missing" after speaking to those pulled from the waves, press officer Flavio Di Giacomo told AFP.

- 'Criminal lunatic' -

An investigation into the shipwrecks has been opened in Agrigento, on the nearby Italian island of Sicily.

Agrigento's chief of police Emanuele Ricifari said the traffickers would have known bad weather was forecast.

"Whoever allowed them, or forced them, to leave with this sea is an unscrupulous criminal lunatic," he told Italian media.

"Rough seas are forecast for the next few days. Let's hope they stop. It's sending them to slaughter with this sea," he said.

As the stormy weather continued Sunday, an alpine rescue team and the fire brigade lifted to safety migrants marooned on a rocky part of Lampedusa's coastline.

The Sicilian Alpine rescue service (CNSAS) said the 34 migrants had been stuck on the rocks since late Friday, after their boat was tossed onto the rocks by strong winds.

They were provided with food, water, clothes and emergency thermal blankets by the Red Cross, but the coastguard was unable to rescue them by sea due to the high waves.

The CNSAS said it had pulled 29 of the 34 people to safety -- including six women, two of whom were pregnant -- while the fire brigade recovered the rest.

- Iron boats -

The Central Mediterranean migrant crossing route from North Africa to Europe is the world's deadliest.

Over 1,800 people have died attempting it so far this year, Di Giacomo said -- almost 900 more than last year.

"The truth is that figure is likely to be much higher. Lots of bodies are being found at sea, suggesting there are many shipwrecks we never hear about," he said.

The number of bodies found has increased in particular on the so-called Tunisian route, which has become increasingly dangerous, Di Flavio said, because of the type of boats used.

Sub-Saharan migrants are being put out to sea by traffickers "in iron boats which cost less than the usual wooden ones, but are utterly unseaworthy, they easily break up and sink", he said.

Migrants also often have the engines stolen from their boats at sea, so that traffickers can re-use them.

The authorities in Tunisia said on Sunday that the bodies of 10 migrants had been found on a beach there, near the city of Sfax.

According to the North African country's interior ministry, 901 bodies had been recovered this year by July 20 following maritime accidents in the Mediterranean Sea, and 34,290 others had been rescued or intercepted.

Nearly 92,000 people have landed on Italy's shores so far this year, according to the interior ministry, more than twice the number over the same period last year.