Under the proposals, 120,000 asylum seekers will be distributed among EU member countries, with binding quotas.
This comes after thousands of mainly Syrian migrants began trekking northwards through Europe this weekend.
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'
The migrant crisis and how to resolve it has exposed divisions within the EU.
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. Vice Chancellor Sigmar Gabriel said his country could cope with 500,000 a year for several years to come.
The planned EU quota system would allocate 60% of migrants 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.
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".