“Europe has not done enough,” the aunt, Tima Kurdi, a resident of Canada, said during a visit on Monday to Brussels for talks with officials. “Germany took the biggest number, and now it has too many. Every country has to take responsibility. Aylan’s death was, I believe, a message from God to the world to wake up and do something about these refugees. Everybody is closing the door in their face.”

All the same, ministers from several East and Central European countries remained steadfast in their opposition to the compulsory distribution of migrants proposed last week by Mr. Juncker.

“This proposal is not solving the problem,” said Robert Kalinak, the Slovak interior minister. The Czech Republic, Hungary, Romania and the Baltic States have all voiced deep reservations about taking in refugees, arguing that they have no tradition of offering refuge to people of different cultures; that their economies cannot sustain the influx; and that most of the migrants want to live in richer and more welcoming places like Germany and Scandinavia.

In a dig at former Communist countries in the East that have said they will take only Christian refugees, Mr. Asselborn, the Luxembourg minister who ran Monday’s meeting, said that even his own country, the European Union’s smallest, “could take in a few hundred people who are not necessarily Christians, who have a different skin color, and that should be able to work in big countries like Poland or the Czech Republic or in Slovakia.”

In an effort to win over opponents of the plan, Germany, France and other nations embraced some of the Eastern Europeans’ tough language, calling for tighter controls of Europe’s external borders and firmer measures against migrants who fail to qualify as refugees, including their swift return to countries deemed safe.

The French interior minister, Bernard Cazeneuve, stressed that economic migrants needed to be separated from genuine refugees fleeing war or oppression. “There cannot be humanity without firmness and responsibility,” he told reporters.