"We're calling on European countries to strengthen their response to the Syrian crisis," said Melissa Fleming, spokeswoman for the UN High Commissioner for Refugees (UNHCR).
"We're urging states to ensure access to their territory, we're urging states to ensure fair and efficient asylum procedures," she told reporters.
Since the conflict began in March 2011, around 123,600 Syrians have sought asylum in Europe, crossing land borders or making risky trips across the Mediterranean.
Under a UN programme, 17 countries have also offered almost 32,000 resettlement places for the most vulnerable refugees, but the UNHCR wants the number to be raised to 100,000 by 2016.
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"Relative to the 2.9 million refugees in countries immediately surrounding Syria, these numbers are small. In fact, they're minuscule. They represent only four percent of Syrian refugees," said Fleming.
"Just to put that into perspective, Europe has a population of 670 million people. Contrast that to Lebanon, which has a population of 4.4 million people and has received 1.1 million refugees," she added.
"Neighbouring countries have reached a saturation point," said Fleming.
She underlined that there had been positive steps in Europe, including a de facto moratorium imposed by most countries on returning refugees to Syria.
But she pointed to "disturbing gaps and practices" including "pushbacks" at land and sea borders by EU members Bulgaria, Cyprus, Greece and Spain, as well as by Albania, Montenegro, Russia, Serbia and Ukraine.
She also criticised slow access to asylum procedures which has left refugees waiting for months in deplorable conditions in over-burdened reception centres.
Under a regional treaty, governments can send refugees back to the European country where they first arrived, but front-line nations such as Italy have pleaded for more help.