Asylum seekers continue to make the risky sea journey from Turkey to the Greek islands. Photo: AP
The head of the UN refugee agency, UNHCR, has urged European leaders to set up a "massive" refugee resettlement programme.
Antonio Guterres said moves to speed up the processing of asylum seekers in Greece was welcome but "not enough".
He was speaking as a new UN report warned that the number of forcibly displaced people worldwide would "far surpass" a record 60 million this year. The EU is grappling to deal with an huge influx of migrants.
More than one million asylum seekers are expected to have arrived in Europe by the end of the year, prompting some states to put up fences and introduce border controls despite the EU's border-free Schengen area.
Mr Guterres said the numbers of displaced people would grow unless conflicts in Syria, Yemen and Libya were resolved.
Earlier this week, the EU agreed to increase the numbers of Frontex border agency staff in Greece, where hundreds of thousands of migrants have arrived by boat.
Many asylum seekers then travel north via the Balkan states without being registered. Mr Guterres welcomed the move but said it was "not enough".
An average of almost 4,600 people worldwide are forced to flee their countries every day And he called for the numbers of refugees being resettled in Europe to be increased.
"We are encouraged by the fact that a number of European countries have been saying, and I believe this is on the table to the European Council, that a massive resettlement programme needs to be put in place for Syrians, but I would expect also for refugees in general," he told a news conference.
"And when I mean massive, I mean hundreds and hundreds of thousands of people, not just what has been discussed until now in relation to resettlement.
"If this is not put in place and the tragedy in the Aegean goes on and the Balkan chaotic situation goes on, I must say I am very worried for the future of the European asylum system."
EU states have agreed to resettle 22,000 people direct from UN refugee camps but so far only about 600 have arrived.
Peter Sutherland, the UN special envoy for migration, also called on European states to take more refugees.
"It is absurd that a continent of 508 million in the EU should find itself unable to deal with what is and should be a manageable number," he told the BBC.
He added: "We have a straightforward moral obligation to take those who are persecuted - which is what refugees are - and to offer them sanctuary."
Friday's report by the UNHCR said "one in every 122 humans is today someone who has been forced to flee their homes".
The figure includes 20.2 million refugees, the highest total since 1992, the UNHCR added. The numbers were mainly driven by the Syrian war, conflict in Ukraine and other protracted conflicts, it said.
The report is based on figures from the first half of 2015. Asylum applications had risen 78% over the same period in 2014, while the numbers of internally displaced people reached an estimated 34 million.
The number of refugees rose by 839,000 in the first six months of 2015 - or almost 4,600 people on average every day.
Europe's migrant crisis is only partially reflected in the numbers, since arrivals have escalated in the second half of 2015, a period not covered by the report.
While the number of refugees is at its highest since 1992, the number of refugees as a percentage of the global population has dropped significantly in that time - from 0.32% in 1992 to 0.21% today.
According to the UN's own statistics, the world's population has increased by more than 1.8 billion in that time.