The U.N. 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.
"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 perilous.
So far, the numbers do not appear to have slowed down as the colder months approach, 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 on Monday, while 30,000 are on Greek islands, most of them on Lesbos, 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.
"I am convinced that with the proper instruments in place, this will be much easier to manage," he told a news conference in Paris.
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 U.N. 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 the Obama administration is taking into account the urgency of the migrant crisis in Europe as it considers further steps that the United States can take.
White House spokesman Josh Earnest declined to discuss the options at a briefing with reporters but said: "Everyone is well aware of the sense of urgency."