Sixteen countries have so far offered places to meet the European Commission's goal announced in September of taking at least 50,000 refugees over the next two years under the bloc's resettlement programme.
"I welcome the strong commitment shown by member states to reduce irregular and dangerous routes and enhance safe and legal pathways," EU migration commissioner Dimitris Avramopoulos said.
"I urge the others to follow soon."
The scheme is aimed at discouraging migrant boats from making the risky Mediterranean crossing, which is still causing deaths more than two years after the migration crisis first hit the continent in 2015.
"We are exiting crisis mode gradually and we are now managing migration in a spirit of partnership and shared responsibility, inside and outside the EU," Avramopoulos said.
The EU also warned of further legal action against three of the bloc's eastern countries if they continue to refuse to accept refugees from Greece and Italy under the quota system.
"I hope that Poland, Hungary and the Czech Republic will take this opportunity to, let's say, revise their position and start relocating refugees," Avramopoulos said.
"If nothing should change, as you know the commission has the power to take things one step further."
The quota scheme, under which member states were required to share the burden of frontline EU states, was wrapping up with just 750 people left in Greece and 3,100 in Italy left to relocate, he added.
The scheme relocated 31,000 out of an originally planned total of 160,000.
The EU has launched a string of plans to tackle the biggest influx of refugees and migrants since World War II, caused initially by people fleeing the conflict in Syria, but now consisting mainly of economic migrants from Africa.
Its policy of helping the Libyan coast guard intercept migrants trying to cross the Mediterranean was condemned on Tuesday by the United Nations, which said they were being sent back to "horrific" prisons in Libya.
"The suffering of migrants detained in Libya is an outrage to the conscience of humanity," UN human rights chief Zeid Ra'ad Al Hussein said in a statement, adding that the policy was "inhuman".
Avramopoulos said he "took note" of the rights chief's comments but added that it "would have been good if he had been in touch with his colleague", the UN refugee chief Filippo Grandi, with whom the commissioner met this week.
"We are working on all fronts to address the dire, really dire situation on the ground in Libya and to protect these people," he said.
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