LONDON — Even as its leaders grapple with populist demands for curbs on migrants, Europe is facing a surge of asylum seekers risking their lives to escape war and poverty in Syria, Afghanistan and elsewhere, according to new assessments on Friday.  The forecast is likely to sharpen disputes between Europe’s mainstream politicians and right-wing figures who campaigned in elections this month on anti-immigrant platforms, scoring remarkable advances and rattling political elites in France and Britain in particular.  The populist gains were built in part on promises to restrict immigration across the 28-nation European Union’s internal frontiers, many of which, under the bloc’s rules, may be crossed at will by citizens of member states.  But in figures released on Friday, Frontex, the union’s border agency, also said the number of migrants from outside Europe known to have entered Europe illicitly this year was already close to the total for all of 2013 and was likely to rise as summer weather brings calmer seas, benefiting migrants crossing the Mediterranean from northern Africa.  For most migrants, packed aboard rickety boats, the journey is a gamble.  “They know that they can drown,” said Carlotta Sami, a spokeswoman for the United Nations refugee agency in Geneva. “They know that they can die.” Only last week, the Italian authorities said they rescued almost 1,000 such migrants in international waters off Sicily and the island of Lampedusa.  But the numbers are nonetheless increasing.  In its annual report issued this month, Frontex said 40,000 asylum seekers arrived, mainly in Italy, from North Africa in all of 2013. But Ewa Moncure, a spokeswoman for the agency, said in a telephone interview that 37,000 migrants had already been detected making the crossing so far this year, according to unofficial figures, while reports in the Italian news media suggested that the figure for the same period was closer to 40,000.  “Looking ahead, everything points to a heightened likelihood of large numbers of illegal border crossings into the E.U.,” the Frontex report said.  Last October, European Union leaders agreed to review the bloc’s procedures for dealing with the influx of refugees. But since the collapse of authority in Libya with the Arab Spring in 2011, much of the onus for dealing with the migrants has fallen to Italy.  After two major maritime disasters that took hundreds of lives last year, Italy increased naval and air patrols as it struggles to cope with the influx. The Italian authorities have also said they are trying to fight the illegal networks that smuggle desperate migrants to Europe.  Greece has tried putting in place a fence along its border with Turkey, an important crossing point for migrants coming from Asia and Africa. But securing Europe’s vast land and sea borders — a task far greater than that faced by the United States along its border with Mexico — has proved to be all but impossible for the European Union, which has prided itself on the relatively free movement of people within its borders.  In 2013, 107,000 people were detected trying to enter the European Union illegally, up from 75,000 in 2012, the report said. Syrians, Afghans and Eritreans were the most commonly detected nationalities, it added. It is not clear how many migrants had escaped detection.  Apart from the central Mediterranean route, there has also been a sharp increase in illegal migration across the border between Hungary, which is a member of the European Union, and Serbia, which is not.  The figures coincided with a series of episodes that illustrated both the determination of asylum seekers to reach Europe and the reluctance of some in Europe to accept them.  This week, the French riot police dispersed hundreds of would-be migrants at a makeshift camp in Calais on the same day as more than 1,000 people tried to force their way over razor-wire barriers into Melilla, a Spanish enclave in North Africa.  The immigration debate played a large part in elections for the European Parliament this month that bolstered the political fortunes of rightist parties in several countries, including Britain, Denmark, France and Hungary.  In France, the right-wing National Front, led by Marine Le Pen, promised to cut the annual number of immigrants to 10,000, down from 200,000, saying that uncontrolled immigration was “a source of tensions in a republic that can no longer assimilate new citizens.”  Public apprehensions about illegal immigration in France have also centered on the status of an estimated 20,000 noncitizen Roma from Romania and Bulgaria.  In Britain, Nigel Farage, leader of the right-wing United Kingdom Independence Party, conjured visions of Romanian organized crime gangs infiltrating his country. “I haven’t got a problem with Romanians,” he told CNBC after the election. “I have a massive problem with Romania.”  The growth of anti-immigrant sentiment is widely seen as dating to 2004, when European Union countries decided to throw open their doors to new members from Eastern and Central Europe. Some countries, like Britain, significantly underestimated the influx that would follow.  At the time, the government predicted that 5,000 to 13,000 migrants would arrive annually until 2010. The 2011 census showed 521,000 Polish-born people listed as residents of Britain, although that number has since fallen. But the arrivals created a perception, fanned by the Euroskeptic media and the far right, that migration was spiraling out of control.  Fears of an immigrant invasion in Britain were fueled anew in January after labor restrictions for Bulgarians and Romanians in nine European Union countries, including Britain, France and Germany, were lifted, prompting concerns that migrants from the bloc’s most impoverished countries were invading. The influx never happened.  John Springford, an expert on immigration at the Center for European Reform, based in London, said that while immigration had been initially welcomed by European policy makers as a means to offset Europe’s aging population, the economic downturn in Britain and elsewhere after the financial crisis of 2008 had spread consternation that immigrants were taking away scarce jobs.  “In the U.K., the recession has given an added piquancy to anti-immigrant backlash,” he said. “There are fears that Romanians and Bulgarians will take away jobs, even as there is little evidence for this.”  Concerns about illegal immigration have prompted some politicians, including Nicolas Sarkozy, the former French president, to call for the bloc to overhaul its current visa-free zone, known as the Schengen area, in which border controls have largely been dismantled.  But Mr. Springford said that while there was new pressure in Europe to tighten immigration policies, Europe’s leaders were nevertheless extremely wary of undermining the free movement of citizens, since it was one of the bloc’s founding principles.  Alan Cowell reported from London, and Dan Bilefsky from Paris.  A version of this article appears in print on May 31, 2014, on page A10 of the New York edition with the headline: European Agency Reports Surge in Illegal Migration, Fueling a Debate. Order Reprints|Today's Paper|Subscribe
The report by the agency feeds a debate on immigration that has led to political gains by far-right parties in the European Union.