"There is no way to resolve a crisis of this dimension if each country acts alone and based solely on its own interests," United Nations High Commissioner for Refugees Antonio Guterres told Portuguese broadcaster RTP.
"Hundreds of thousands of refugees have arrived in Europe since the beginning of the year," said Guterres, a former Portuguese prime minister.
"But the European Union counts 500 million inhabitants. If there was a real policy of solidarity, the problem would be easily handled."
Despite so far failing to reach a deal on the larger figure, EU ministers last week formally approved a plan first floated in May to relocate 40,000 refugees from Greece and Italy.
The UNHCR has estimated that at least 200,000 relocation spots will be needed by the end of 2016, and spokeswoman Melissa Fleming said Tuesday that number would likely need to be revised upwards.
"We believe this may be the last opportunity for a coherent European response to manage a crisis that is increasing suffering and exploitation of refugees and migrants and it is also increasing the tension between countries," she told reporters in Geneva.
The UN agency has proposed a number of measures for addressing the crisis, including the immediate creation of facilities and Greece and expansion of existing facilities in Italy with the capacity to receive, assist, register and screen the hundreds of thousands arriving by sea.
Nearly 2,900 have died trying, according to the International Organization for Migration.
Guterres also stressed the importance of a proper registration procedure, to make it possible to "distinguish the refugees from those who are not".
This way, people entitled to refugee status could take part in the relocation programme under discussion, while those not considered refugees could be "sent back to their countries of origin in a way that respects their dignity," he said.