At least one of the men who carried out suicide attacks in Paris last month came through the Balkans to western Europe posing as a Syrian refugee, counter-intelligence and police sources have said.
But before the Paris attacks, many European countries were already talking about closing their borders to refugees - or actually doing so - because of the sheer weight of numbers.
Much of the rhetoric connecting refugees and acts of violence has come from the United States, where Ben Carson, a 2016 Republican presidential candidate, likened Syrian refugees to "a rabid dog running around your neighborhood," and said admitting them would put Americans at risk.
His rival candidate Donald Trump suggested shutting mosques to prevent Muslims in the United States from becoming radicalized.
After the attacks in Paris, the U.S. states of Texas, Arkansas, Alabama and Michigan said they would close their doors to Syrian refugees, and the U.S. House of Representatives voted overwhelmingly to suspend President Barack Obama`s program to admit 10,000 Syrian refugees and intensify the process of screening them.
Guterres, a former prime minister of Portugal, said he was sympathetic to governments` impulse to rely on counter-terrorism strategies, but it would be an illusion to think that counter-terrorism and military action alone would solve the problem.
"An essential part of this is to convince the potential recruits of terrorist organizations that that is not the way to express their own anger or their own concerns or their own perspectives," said Guterres, who was speaking at the launch of a record $20.1 billion U.N. humanitarian appeal for 2016.
Attacks in Europe may be linked to one or two people who had entered with the huge refugee influx, but it was essentially a home grown problem that would not be solved by closing borders, he said.
"The more it is said or the more it is done in hostility to Syrian refugees because they are Muslims, the more the chances for (Islamic State) and other groups to recruit within the borders of European countries people to do the kind of nasty things we are now witnessing."
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