Many European Union countries oppose obligatory quotas that would force them to take in refugees from other overwhelmed member states, European Council president Donald Tusk has said.
Mr Tusk said: “There is no enthusiasm for obligatory quotas. But we should all show solidarity and do what we can to help.”
EU members voted last year to share responsibility for an estimated 160,000 asylum seekers who have flowed into Europe, concentrating primarily in Italy and Greece.
More than a year later, just over 6,000 refugees have been relocated to other countries.
Hungary, which voted against the sharing plan, has challenged the scheme in court. Mr Tusk’s home country, Poland, also has opposed it.
Earlier, international aid group Doctors Without Borders said refugees at camps in Greece were still living in mostly “appalling conditions”.
In a report, the agency commonly known by its French name, Medecins sans Frontiers (MSF), argued that the EU and Greece had “collectively failed to establish humane and dignified reception conditions”.
Around 14,000 migrants are confined to islands in the eastern Aegean Sea where they are being processed for potential deportation back to nearby Turkey.
At the rubbish-strewn refugee camp of Ritsona, 50 miles north of Athens, children walk barefoot and families in tents use wooden pallets for flooring, to stay above the mud and try to stay warm.
“It’s very bad. How can I explain: I mean very bad,” Syrian refugee Yousef Hanash said.
“Can you imagine living in a tent with six persons and, if you have a newborn baby, how the situation will be?”
Mr Hanash said he came to Europe as a last resort, unable to keep his family safe after his cheese factory was destroyed in the war and he moved around Syria.
MSF said people at risk included pregnant women and people with mobility problems, while it described conditions facing mental health patients as “dire”.
“For vulnerable people, the lack of appropriate accommodation and specialised care is directly contributing to their worsening health status and could well be life-threatening,” the group said.
“For the victims of violence or other forms of ill-treatment and people with psychiatric disorders, inadequate living conditions further undermine people’s efforts to re-establish a sense of normality and safety and to engage in a therapeutic process.”
The group urged the government to seek alternatives to the refugee camp system and improve a screening process to identify vulnerable migrants, while it said the EU needed to provide emergency financial support to the state health system.