European Commission President Jean-Claude Juncker is due to announce plans to tackle the migrant wave which has thrown European policy into disarray.
Under the proposals, 120,000 additional asylum seekers will be distributed among EU nations, with binding quotas.
This comes after a surge of thousands of mainly Syrian migrants pushed north through Europe in recent days.
Germany, the main destination for many migrants, supports quotas, but some EU countries oppose a compulsory system.
Hungary has been warned to expect an additional 40,000 migrants by the end of next week.
Vincent Cochetel, a regional co-ordinator for the UN refugee agency UNHCR, also urged the Hungarian authorities to improve registration and reception procedures.
Hungary has become a key point on the journey north for the migrants, with more than 150,000 people arriving this year.
The authorities there are now reinforcing a border fence designed to keep migrants from entering from Serbia and are toughening asylum laws.
In a separate development Australia, which has been under pressure to do more to help displaced people, has announced plans to take in more Syrian refugees.
The government said it would accept 12,000 Syrian refugees from persecuted minorities.
‘Important first step’
Mr Juncker’s plans expand upon quotas for the relocation of 40,000 migrants in Italy and Greece proposed in May – though governments only actually agreed to take 32,000.
The fresh plans for an extra 120,000 migrants would allocate 60% of those now in Italy, Greece and Hungary to Germany, France and Spain, reports say.
The numbers distributed to each country would depend on GDP, population, unemployment rate and asylum applications already processed.
Countries refusing to take in migrants could face financial penalties.
The migrant crisis and how to resolve it has exposed divisions within the EU.
Image copyright AP Image caption Hundreds continue to enter Macedonia as they head north
The Czech Republic, Slovakia, Poland and Romania have opposed the idea of mandatory quotas.
On Tuesday, though, Poland appeared to soften its position. Prime Minister Ewa Kopacz said the country would accept more migrants than the 2,000 it first offered to take.
Germany has welcomed Syrian migrants, waiving EU rules and saying it expects to deal with 800,000 asylum seekers this year alone – though not all will qualify as refugees and some will be sent back.
Vice Chancellor Sigmar Gabriel said his country could cope with 500,000 a year for several years to come.
Also planned are measures to help the economies of countries in the Middle East and Africa, and deter people-smugglers.
German Chancellor Angela Merkel said on Tuesday that quotas were an “important first step”.
Speaking alongside the visiting Swedish Prime Minister, Stefan Lofven, she added that the EU needed an open-ended “system to share out those with a right to asylum”.