UPDATED Thursday pm: Around 200 migrants are believed to have died after yesterday's shipwreck off Libya, with hopes of finding more survivors fading.

The hundreds who survived have been taken to Italy.

Among those rescued was a Palestinian man who saved his wife by giving her his life jacket, then diving below the surface to grab their toddler daughter as she disappeared.

"Those that were on deck would have managed to jump, some of them drowned and some of them were saved," said Martin Xuereb, director from the Malta-based Migrant Offshore Aid Station, one the groups involved in the rescue effort.

"I think it's unlikely that any additional survivors will be picked up."

Military vessels and aircraft from a multi-nation operation were searching waters off Libya, a day after the 20-metre boat overturned as rescuers were approaching. With seas warm and calm, rescuers expressed hopes others might be alive.

In the first hours after the accident yesterday, 367 survivors were rescued and 25 bodies recovered.

Times of Malta photographer Darrin Zammit Lupi, who is on embedded on the MOAS vessel said the sea was very calm this morning and more activity was expected. Meanwhile the search for bodies goes on.

The UNHCR said the boat had been packed with people “in every nook and cranny”.

Military officials from Ireland, whose navy vessel the Le Niamh was among those at the scene, said they were given an initial estimate of 600 migrants aboard the smugglers' boat. If that estimate holds, as many as 200 migrants might have drowned.

At least 367 survivors were taken aboard the Le Naimh, which was approaching the dock at Palermo, Sicily, by late afternoon.

The Italian Navy, which had two ships in the rescue operation, said three survivors were flown by helicopter for medical treatment aboard the Doctors Without Borders ship Dignity1. One was a man with a fractured leg; the other was a mother, with one-year-old son, who needed dialysis.

Three other injured survivors were flown out by another navy helicopter to a hospital on the tiny Italian island, Lampedusa, south of Sicily.

When the Dignity1 arrived at the capsizing site, it was hard to tell how many were in the water, said Juan Matias Gil, a Doctors Without Borders search and rescue operations field co-ordinator.

"All in all, there were no more than 50 people" in the water, Mr Gil said. "There were some bodies floating, so it was quite a shocking scene."

During the rescue, crew of Dignity1 tossed life vests and life preservers as survivors swam frantically to boats.

Video made aboard Dignity1 and released by Doctors Without Borders showed the Palestinian family. The mother caressed the hand of her daughter Azeel, a little more than one year old, as the father, Mohammed, sat next to them.

"They all went into the water, with only one life jacket," Mr Gil said. "So this life jacket was with the father, who gave the life jacket to his wife, because she didn't know how to swim. After that he saw that the baby was getting deep in the water" and in danger of drowning.

"After he came out with the baby, they were seen, they were rescued and they were brought aboard" Dignity1, Mr Gil said.

Several Syrians were among those rescued, including a pregnant woman who at first appeared in danger of miscarriage.

The incident took place some 22 nautical miles north of Zuwarah, a major point of departure for many fleeing Libya.

Should the figures be confirmed it would be the biggest migrant incident since 850 migrants drowned in a single incident last April. The incident sparked a major EU effort to provide migrants rescue off Libya, from where thousands have fled amid unrest. 

In a statement last night, Amnesty International said European governments must do more to provide safe and legal ways for people in need of protection to enter the EU rather than risking their lives at sea in their thousands.