ROME (AP) — Desperate choices faced a Palestinian family who were tossed off a capsizing boat full of migrants into the Mediterranean Sea, with just one life jacket.

The father’s heroic effort to save his wife and their toddler was among the most dramatic stories to emerge from two days of disasters for migrants attempting to cross the Mediterranean.

The father gave his life jacket to his wife, who couldn’t swim, then dived below the surface to grab their toddler daughter as she sank.

Officials said the family was among 373 people who were saved after a fishing boat loaded with hundreds of migrants overturned on Wednesday, though 25 bodies were also recovered.

On Thursday, 381 people were saved by the Italian coast guard before their boat sank off the Libyan coast. In another rescue, the Italian navy plucked to safety 101 people who were crowded aboard a rubber dinghy in danger of sinking.

On Thursday, smugglers took advantage of calm seas to send out a flotilla of boats, pushing the number of migrants needing rescue past 1,000 for the day. Among the boats were two small vessels which reached the Sardinian coast, including near the tourist and fishing island of Sant’Antioco.

Video made aboard the ship Dignity1 and released by Doctors Without Borders showed the family recovering from their ordeal. The mother kissed the hand of her daughter Azeel, a little more than a year old. The father, Mohammed, sat next to them.

“They all went into the water, with only one life jacket,” said Juan Matias Gil, a Doctors Without Borders search and rescue operations field coordinator. “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, Gil said.

Military vessels and aircraft from a multi-nation operation were searching waters off Libya on Thursday for any more survivors from Wednesday’s incident. Warm, calm seas inspired hope of finding more survivors, but none had been found by evening.

In a separate rescue Thursday morning, all 381 people aboard a fishing boat in difficulty off the Libyan coast were taken aboard the Italian coast guard vessel Fiorillo, the coast guard said. Shortly after the Fiorillo set sail to bring the survivors to Italian shores, the fishing boat sank, the coast guard said.

Military officials from Ireland, whose navy vessel the Le Niamh was among the vessels on the scene Wednesday, 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.

The Le Niamh docked in Palermo, Sicily, late Thursday afternoon with 367 survivors aboard, along with 25 plain wooden coffins. Six other survivors were evacuated by helicopters for treatment.

As the Le Niamh pulled in, a little boy, peering between the metal railing of the ship, waved and gave a thumbs up sign. A young girl, her head jerking back, appeared to collapse as she was scooped into the arms of one of the land-based personnel helping the survivors disembark.

“Some of the people are torn by grief. They lost their children, they couldn’t find them” in the seas, Giovanna Di Benedetto, a spokeswoman for the organization Save the Children, told Italian state TV on Palermo’s pier.

Five crew members of the capsized vessel were among those disembarking, the Italian news agency ANSA said, and Palermo police were questioning the men — Libyans and Algerians — as smuggling suspects.

Irish officials 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.

When the Dignity1 arrived at the site, it was hard to tell how many were in the water, Gil told The Associated Press in Rome via Skype.

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

The crew of Dignity1 tossed life vests and life preservers as survivors swam frantically to boats. One survivor, without a life vest, was spotted floating on his back. The puffy hood on the man’s soaked windbreaker appeared to have helped him stay afloat.

All of the nationalities of the survivors weren’t immediately available.

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

It may never be known how many people might have been trapped on lower decks of the boat when it overturned.

Gil noted these fishing boats favored by smugglers have two lower decks.

“If you are in the floor downstairs, it is impossible to go out if the boat capsizes. So surely all these people — they were stuck inside the boat when the boat went down,” the Doctors Without Border official said, referring to past experiences.

Efforts to recover bodies from a horrific capsizing on April 18 off Libya, also when rescuers approached, are still being conducted, the Italian navy said. Investigators said as many as 800 were aboard. A special navy diving operation eight bodies from near the wreck lying on seabed weeks after the sinking. Only 28 people survived, including two suspected smugglers.

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Frances D’Emilio can be followed on Twitter at www.twitter.com/fdemilio