But Mr. Di Giacomo also raised the possibility that the new wave of Pakistani migrants was drawn from a longstanding population of Pakistani migrant laborers inside Libya, which has been a destination for Pakistani workers since the time of Col. Muammar el-Qaddafi, who was ousted during the Arab Spring in 2011.

The deteriorating conditions in Libya could have compelled the Pakistanis to abandon the country and make the sea crossing, Mr. Di Giacomo said. “They find themselves stuck in a horrible situation, vulnerable to human rights violations and the slave market. So they may have no choice but to seek a crossing to Europe.

“We have to investigate whether they have been living in Libya for years, or coming more recently through Turkey and Sudan,” he said.

Leonard Doyle, a spokesman for the migration agency, said another possible reason the growing number of Pakistanis, as well as Bangladeshis, making such journeys could be the increased use of social media to better connect with people willing to attempt the trip.

There was no immediate reaction from the Pakistani government on Friday.

Pakistan has previously said that it is taking measures to reduce people-smuggling and illegal migration. Its embassy in Athens wrote to officials in Islamabad in January, according to local news outlets, appealing for additional help to curb migration.

Pakistanis have been traveling to Europe illegally for decades. Traditionally, the bulk of them come from Punjab, the country’s most populous province. From there, the journey has usually involved going first to the southwestern province of Baluchistan and then, illegally, into Iran and onward toward Europe.

At least 246 migrants died trying to cross to Italy in January, the United Nations says, so the disaster on Friday means that the number of people killed while trying to reach Europe this year will almost certainly surpass 300.