The European Commission, the EU executive, unveiled options to reform the rules two days after Greece began to expel migrants to Turkey under a controversial deal between Brussels and Ankara. The returns have since stalled.
"We need to reform our European asylum system," the commission's First Vice President Frans Timmermans told a press conference in Brussels. "The present system is not working."
The existing so-called Dublin rules have been criticised as obsolete and unfair to countries like Greece, where most of the 1.25 million Syrian, Iraqi, Afghan and other migrants entered the bloc last year.
But -- as 2015 showed -- the rules fell apart when countries like Italy and Greece, one of the poorest EU members, were overwhelmed by migrants who wanted asylum in Germany and other wealthy northern EU countries.
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"This is neither fair, nor sustainable," Timmermans said, adding it was a "huge burden" to frontline countries.
Under one reform option, if a member state faces "disproportionate pressure" from migrant arrivals in the future, a "corrective fairness mechanism" can be introduced to redistribute migrants within the bloc.
However, EU states have already struggled to implement an emergency scheme agreed last September to relocate 160,000 asylum seekers out of Greece and Italy. Only 1,100 of these have been resettled so far.
The delays have been pinned on a range of factors, from governments trying to filter out jihadists from among the refugees following the terror attacks in Brussels and Paris, to a lack of housing and education -- but, say sceptics, political foot-dragging has also played a part.
Under a second, more drastic option, a "permanent distribution key" would be introduced based on the population and wealth of each member state.
The diplomat said the second option is less popular, supported mainly by Germany and Sweden, which have already admitted the lion's share of migrants who did not want to stay in Greece and Italy.