At least 850,000 people are expected to cross the Mediterranean seeking refuge in Europe this year and next, the United Nations said on Tuesday, giving estimates that already look conservative.
The UN refugee agency UNHCR called for more cohesive asylum policies to deal with the growing numbers.
Many are refugees from Syria, driven to make the voyage by intensified fighting there and worsening conditions for refugees in surrounding countries due to funding shortfalls in aid programs, UNHCR said. Hundreds have died at sea.
"In 2015, UNHCR anticipates that approximately 400,000 new arrivals will seek international protection in Europe via the Mediterranean. In 2016 this number could reach 450,000 or more," it said in an appeal document.
Spokesman William Spindler said the prediction for this year was close to being fulfilled, with 366,000 having already made the voyage. The total will depend on whether migrants stop attempting the journey as the weather gets colder and the seas more dangerous.
So far, the numbers do not appear to have slowed down, with many appearing spurred on by Germany's announcement that it will ease the rules for Syrians seeking refuge who first reach the European Union through other countries.
A single-day record 7,000 Syrian refugees arrived in the Former Yugoslav Republic of Macedonia (FYROM) on Monday, while 30,000 are on Greek islands, most of them on Lesvos, it said.
Many arrive first in Greece, then leave the EU to travel up through the Balkans to Hungary and onward to Germany.
"So obviously the discussions this week in Europe are taking even on greater urgency because it obviously cannot be a German solution to a European problem," UNHCR spokeswoman Melissa Fleming told a news briefing.
UNHCR chief Antonio Guterres called for an increase in the number of legal ways for refugees to come to Europe, such as an increase in number of visas and ways to reunite people with their families.
Germany told its European partners on Monday they must take in more refugees as it handles record numbers of asylum seekers.
The European Union's executive Commission is expected to unveil a program this week that would redistribute 160,000 asylum seekers who arrive in Italy, Hungary and Greece.
Peter Sutherland, special representative of the UN secretary-general for migration and development, called for a "harmonized system" and "fair allocation" in the European Union.
He said Europe's "Dublin rules" requiring asylum seekers to apply in the first EU country they reach would have to be amended, or they could jeopardize the principles of border control-free travel in the bloc's Schengen zone.
"Coherence is going to require leadership and leadership before we see the destruction of great achievements like the Schengen agreement," he warned. "I think Dublin doesn't work."
Other countries – including the United States, wealthy Gulf states and Japan – must face their responsibilities, he said.
The White House on Tuesday said it was considering steps to ease the crisis. Spokesman Josh Earnest declined to discuss the options at a briefing with reporters but said: "Everyone is well aware of the sense of urgency."
Australian Prime Minister Tony Abbott bowed to pressure from critics on Wednesday and said Australia would accept 12,000 refugees from Syria on top of its current humanitarian intake quota of 13,750 – and extend air strikes against Islamic State militants in Iraq into Syria.
Germany's decision last month to open its doors to Syrians who arrived elsewhere in the EU has brought the issue sharply into focus, as did images last week of a drowned Syrian toddler washed up on a Turkish beach, which appeared on newspaper front pages across the continent.
Germany alone expects 800,000 asylum applications this year, including those who have crossed the Mediterranean, others from Balkan states and some who arrived in previous years.
German Chancellor Angela Merkel said on Tuesday that Europe needed to implement a joint system for dealing with asylum seekers and agree to binding quotas on how to distribute refugees across the continent.
"This joint European asylum system cannot just exist on paper but must also exist in practice. I say that because it lays out minimum standards for accommodating refugees and the task of registering refugees," she told a joint news conference with Swedish Prime Minister Stefan Lofven in Berlin.
"Our responsibility is deeply moral. It is a human responsibility," he said. "We have to do this together. There are 28 countries in the EU with the same responsibility."
German Vice Chancellor Sigmar Gabriel said on Monday that if countries in eastern Europe and elsewhere continued to resist accepting their fair share of refugees, the Schengen system would be at risk.
Austria meanwhile said it would improve accommodation for asylum seekers as winter approaches and increase capacity at refugee-processing centres in anticipation of tens of thousands of new arrivals.
Smaller central and eastern European Union states have rejected any mandatory quotas for taking in refugees as the European Commission prepares to present a plan to that end.
Poland however indicated it could accept more migrants than the 2,000 it announced earlier. Spain said it was ready to accept as many refugees as the Commission proposes, reversing course after saying it was being asked to take too many.
Britain, which is exempt from common EU asylum policies, announced this week it would take thousands of refugees directly from camps in the region, but not from among those who have reached other EU countries.
Britain has taken in fewer Syrians than other EU countries but has given Europe's biggest donations in aid to the region, arguing that this is more effective assistance.
Four million Syrians are registered as refugees in Turkey, Lebanon, Jordan and Iraq. Another 8 million are displaced within Syria itself.
UNHCR's Fleming welcomed separate offers announced by Britain and France on Monday to take in Syrian refugees, but said reception centers must be set up in countries including Hungary, Greece and Italy to process asylum claims.
"Those can only work if there is a guaranteed relocation system whereby European countries saying yes will take X number. We believe it should be 200,000 – that's the number we believe need relocation in Europe countries," Fleming said.
Noting that Europe has a population of half a billion, she added: "It is a manageable situation if the political will were there."
She also appealed for more aid for UN programs for displaced Syrians within the Middle East, saying funding problems were creating conditions that encouraged refugees to leave the camps for Europe.
The UN World Food Program's operation to feed Syrians costs $26 million a week, but it has cut rations to 1.3 million refugees due to a funding shortage, spokeswoman Bettina Luescher said. "Basically now the refugees are living on around 50 cents a day in those countries around Syria."