As European states have tightened borders following the arrival of more than a million migrants by sea last year and the Athens government has appealed for help to house and care for tens of thousands still arriving and now stranded in Greece.
The European Commission's proposal will, if approved, switch 300 million euros this year from its 155-billion euro annual budget to the new emergency assistance scheme and 200 million euros both next year and in 2018.
Officials stress that the programme will not divert funds from the EU's 1.1-billion annual budget devoted to helping the world's poorest. They note that relieving the suffering of refugees closer to their homes is a key part of the 28-nation bloc's strategy to discourage people from making dangerous journeys to Europe.
More than 400 people have died or gone missing in the Mediterranean this year as they tried to reach Europe, most of them on the short but perilous crossing from Turkey to Greece. Turkey is at the heart of the EU's efforts to slow the influx of refugees and migrants and the bloc wants Ankara to ensure that daily arrivals fall below 1,000 from 2,000-3,000 at present.
Two officials said that Germany, the principal destination for those arriving in Europe, is looking for flows to be "in the realm of three digits, not four" per day and, should that happen, Berlin would start taking refugees directly from Turkey for resettlement - an attempt to promote legal migration rather than continuing the chaotic influx of 2015.
The Commission also said that 308 irregular migrants who had no case for asylum in Europe were being returned to Turkey from Greece, a sharp increase on recent numbers going back to Turkey.
The EU money, to be spent in conjunction with the United Nations NGOs and private charities working in Greece and other EU states, is intended to fund purchases of shelter, food, medical aid and other basic services.
Greece, which now houses about 25,000 refugees and migrants, has hitherto benefited from EU funding and assistance under other programmes to bolster its border and security systems and coordinate donations of aid from fellow EU members, though Athens has complained that offers have been inadequate.
"The number of refugees continues to rise, so do their humanitarian needs. All of this is happening inside Europe," Humanitarian Aid Commissioner Christos Stylianides said.
At a single border point, the Idomeni crossing between Greece and Macedonia, between 12,000 and 15,000 stranded people were in need of urgent humanitarian assistance, he said. Officials in Brussels said the aim is to have the scheme operational on the ground "within weeks rather than months".
The new programme, to be a permanent feature of the EU budget, is intended for use by any EU state that is "overwhelmed" and cannot cope with a wide range of emergencies, including accidents, militant attacks and epidemics. It will need approval by the European Parliament and member states.