EU member states have been asked to take in 40,000 Syrian and Eritrean asylum seekers who land in Italy and Greece over the next two years.
Germany, France and Spain would receive the most migrants under the European Commission's plan, published on 27 May.
The UK government says that it will not take part in any quota system, while France, Spain, Hungary, Slovakia and Estonia have also all voiced concerns. A final decision will be taken by EU governments after a vote by MEPs.
Denmark has the right to opt out of the plan while Ireland and the UK can decide whether they wish to opt in.
Of the 40,000 migrants considered "in clear need of international protection", the Commission says Germany would take in 8,763 (21.91%), France 6,752 (16.88%) and Spain 4,288 (10.72%).
Dimitris Avramopoulos, the home affairs commissioner, said it was not proposing "the fixing of quotas... for migration in general", but it was "up to each member to decide how many refugees they will grant refugee status [to]".
"We only propose - and we insist on that - a fair distribution of a concrete number of migrants in clear need of international protection across the European Union," he said.
Countries would receive €6,000 (£4,250) for every person relocated on their territory under the latest proposal, the commission said.
British International Development Secretary Justine Greening echoed Home Secretary Theresa May by rejecting the plan out of hand. She said the quota plan could act as a "pull for more migrants".