"Unfortunately, we have now reached a milestone whereby over 2,000 migrants and refugees have died as of this past weekend," International Organization for Migration spokesman Itayi Virri told reporters in the Swiss city.
The organization said around 188,000 people had been rescued so far this year trying to cross the Mediterranean, and warned the 200,000-mark could be crossed by the end of the week.
IOM said the latest toll confirms "this route as the deadliest for migrants in search of a better life," and warned the situation was worsening.
Up until the end of July last year, more than 1,600 migrants perished trying to make the journey, with 3,279 dying throughout the whole of 2014.
Nearly all of the people crossing the Mediterranean so far this year, often in rickety boats and at the mercy of human traffickers, have landed either in Italy (97,000) or Greece (90,500), the IOM said.
Virri said the so-called central Mediterranean route had proved by far the deadliest, with just over 1,930 people dying trying to cross from Libya to Italy so far this year, while only about 60 had died trying to reach Greece.
The eastern route is shorter and IOM said that traffickers taking people to Italy tended to use more unseaworthy vessels, leading to the higher death toll.
Nineteen people lost their lives in the Channel of Sicily last week alone, with the bodies of 14 migrants brought to the Sicilian port of Messina on July 29th.
They had been travelling with 456 others who were rescued.
And on Monday, 550 migrants rescued in the Mediterranean over the weekend arrived in Sicily aboard a ship operated by Doctors Without Borders (MSF), which also carried the bodies of five people who died at sea.
The victims, four women and one man, were found dead on a boat that was rescued on Saturday with 112 people on board, and appeared to have died of dehydration.
While lamenting the tragic milestone of more than 2,000 deaths, Virri pointed out that increased European Union efforts since April to rescue migrants at sea meant "a lot of people have been saved who otherwise would have lost their lives."
Many of those risking their lives to cross the Mediterranean travel on to other European countries, with a number of them setting their sights on Britain, which along with France is grappling with a migrant crisis of its own.
The migrant crisis in the northern French port of Calais has hit the headlines in the past week, with hundreds of people desperate to reach Britain making attempt after attempt to breach Eurotunnel defences, some paying for it with their lives.
Last week, a Sudanese man in his 30s died, apparently crushed to death by a lorry, and at least 10 people have been killed since June trying to get through the Channel Tunnel to Britain where many already have family and work is perceived as easier to find.
Police said some 600 attempts were made to get into the tunnel from the Calais side overnight to Tuesday, and around 1,700 attempts were made the night before.
Between 3,000 and 5,000 migrants are meanwhile reported to be camped out in Calais waiting for a chance to cross to Britain, and IOM on Tuesday urged Europe to seek broader, long-term measures to address the wider migrant crisis affecting the continent.
It cautioned that "stop-gap measures such as fences and barriers being planned or erected in the EU", including at Calais, would not stop irregular migration but would put vulnerable migrants more at risk of falling prey to smugglers.
"Europe has a moral and a historic responsibility to respond in a humanitarian way," IOM regional director for the EU Eugenio Ambrosi said in a statement.