Mr. Asfour and his sister-in-law Samah Asfour, the mother of one of the cousins, Raed, 17, went to the money changer together and paid $2,000 for each of the four. Mrs. Asfour said that the usual cost was $1,500, but that the money changer had told her that the extra cash would ensure their sons a place on a large, sturdy ship, not a small one that could sink.

“We paid more so our boys would be safe,” she said. They were hoping to find medical treatment, jobs and a better future than the one they saw for themselves in Gaza. “They went for treatment. Why would we send them there?” Mrs. Asfour said. “This country doesn’t care for them, and they are desperate. They were seeking a good life.”

Mr. Asfour said he spoke to one of the smugglers in Egypt on his son’s mobile phone. “I asked him to take care of Ahmed because of his special situation,” Mr. Asfour said. “The smuggler told me not to worry and said Ahmed should only bring with him boxes of bottled water and juice and a box of dried dates.”

Other Gazans described how relatives left through the tunnels at Rafah in groups organized by a smuggler, paying him $1,500 per person and $2,000 for the boat runners.

The International Organization for Migration, based in Geneva, says records show that around 2,900 Palestinians have reached Italy this year, most of them in July and August.

Only 11 people are known to have survived the sinking of the rammed vessel, eight of them Palestinians from Gaza, and accounts from relatives of others aboard the doomed ship suggest that most of the passengers were Gazans, according to Joel Millman, a spokesman for the migration organization. He said the office had received a constant stream of calls from Gazans desperately seeking news of family members.

Relatives in contact with some of the migrants as they prepared for the journey said they had been driven in buses carrying 90 to 100 people to an Egyptian port, Damietta. Those aboard the boat included around 100 children younger than 10 who were stuffed below the deck, the migration organization reported.