The UN refugee agency, as well as aid agency Medecins San Frontieres, say anywhere from 700 to 900 migrants may have died at sea this week making the journey from Libya toward Italy. (Reuters)

More than 700 migrants died in the Mediterranean Sea last week as their boats foundered, aid and refugee agencies estimated Sunday, with most of them attempting to flee the Libyan coast for Italy in the deadliest period of migration to Europe this year.

The sinkings raise concerns that Europe is facing yet another summer with an overwhelming surge of new arrivals and intensify the debate over how to handle them. Although the migrant influx tends to slow during the winter and early spring, waters are growing warmer and calmer: Over the past week alone, 15,000 people arrived in Italy, many of them pulled to shore in dramatic emergency naval or coast guard rescue operations.

“This is the beginning of the peak season,” Federico Fossi, a spokesman for the United Nations’ refugee agency, said by phone from Rome. “It’s intense.”

Fossi cautioned that the death toll from last week was an estimate based on accounts from survivors. But he said that in the span of three days starting last Wednesday, there were three ­separate and deadly shipwrecks about 35 nautical miles from Libya. Photos from one rescue showed a trawler flipping over, shoveling hundreds of people into the sea. The week was probably the deadliest in the Mediterranean since April 2015.

Of last week’s sinkings, the most catastrophic occurred on an engineless vessel tied with rope to a fishing boat. About 500 migrants were on the fishing boat and 600 more were on the vessel being towed, Fossi said. When it began to sink, several dozen passengers were rescued or managed to climb aboard the other boat. But 550 died or were left missing.

Video from the Italian Navy shows a large ship capsizing off Libya's coast on May 25 with more than 500 migrants aboard. (Italian Navy)

According to several accounts from news wire services, a Sudanese captain ordered the cutting of the rope between the two vessels as the trailing one began to take on water. That captain was arrested after his arrival in Pozzallo, a port town in Sicily.

“And let me tell you — this is quite a new thing,” Fossi said. “We have never seen that before — a boat without an engine tied by a rope to the other one. That shows you the human traffickers are becoming really, really greedy and cynical and merciless. Tying a boat to another one is really dangerous.”

Last year, according to the U.N. High Commissioner for Refugees (UNHCR), about 3,800 people died or vanished at sea trying to make it to Europe. This year, after accounting for the latest sinkings, the number stands above 2,000.

War, repression and government collapse in parts of the Middle East and Africa have caused what many consider to be the worst migration crisis since World War II. In 2015, more than 1 million migrants tried to enter European Union countries. This year, nearly 200,000 have arrived on Europe’s shores.

The influx has tested the con­tinent’s ability to cope and has provided fertile ground for politicians favoring tighter border controls and decreased European integration. Hungary has built razor-wire fences along its borders with Serbia and Croatia. A right-winger vowing to “stop the invasion of Muslims” was narrowly defeated in Austria’s presidential race. Those who favor the British exit from the European Union — the nation votes on the matter next month — say such a move would allow vastly tighter border control.

According to the Associated Press, quoting Britain’s Home Office, 18 migrants coming from Albania were rescued this week from an inflatable boat that ran into trouble in the English Channel.

Although a large-scale exodus from Syria is partly responsible for the unparalleled flow, the routes between Libya and Italy have tended to transport Africans — particularly Nigerians, Eritreans and Somalis. Aid workers have speculated that Italy, rather than Greece, could emerge this year as the primary starting point for migrants, following the tightening of borders between Greece and its northern neighbors. That has effectively thwarted migrants from moving into the more prosperous parts of northern Europe. Last month, Greek and European Union officials also started deporting migrants to Turkey.

Those who have survived the latest wrecks have been taken to Italian port cities, given food and blankets and, in some cases, received medical treatment. But Italy — with a sagging economy and an unemployment rate of 11 percent — has also been strained by the influx, particularly as Austria has tightened its own border controls along a path that migrants have taken en route to more-welcoming countries such as Germany and Sweden.

Italy is bracing to house tens of thousands of people while processing more asylum seekers, a duty it shrugged off in the past.

“The pressure is on the Italians to deal with them” and process the asylum seekers as they’re supposed to, said Leonard Doyle, a spokesman for the International Organization for Migration. “If in the past they’ve been turning the blind eye and encouraging people to skedaddle, the political situation is a bit different now.”

Compared with Syrians, who are fleeing a particularly dire situation, Nigerians and other Africans arriving in Italy face steeper odds for winning asylum claims, analysts say. But Europe is also unlikely to send migrants back to Libya, where competing governments have fought recently for power and the Islamic State has gained a foothold. Europe also doesn’t have a “readmission” agreement with Libya for returning migrants.

“So, what to do with these people next — that is a huge, huge question mark,” said Matteo Gara­voglia, the Italy Program fellow at the Brookings Institution’s Center on the United States and Europe.