BRUSSELS (Reuters) - EU states should be permitted to send some asylum-seekers back to Greece from March, the bloc’s executive said on Thursday as it looks to restore a common policy on migration that collapsed last year under a mass influx of refugees.

European Commission First Vice-President Frans Timmermans addresses the European Parliament during a debate on the commission work Programme for 2017, in Strasbourg, France, October 25, 2016. REUTERS/Vincent Kessler

Under EU rules, the first country of entry should handle an asylum-seeker’s claim, but that system broke down in 2015 when Greece was overwhelmed by the arrival on its shores of most of the more than 1 million people who entered Europe.

Athens let many of them pass through unprocessed. That led some other EU countries to close their borders, stranding many people in Greece, which struggled to offer proper shelter. Some 62,000 migrants are still there.

“Asylum seekers need to know that they cannot relocate themselves and that if they do so, they will be sent back,” EU migration chief Dimitris Avramopoulos - himself a Greek - told a news conference.

But it also would be “totally irresponsible” to increase the burden on Greece, which other EU states needed to show a greater willingness to share, he said.

In Athens, a spokesman for the Greek government declined immediate comment.

Last year’s influx of migrants also undermined the principle of freedom of movement within the EU as many other member states imposed entry restrictions and, in some cases, erected border fences.

Thursday’s Commission recommendation, which member states are not obliged to adhere to, refers only to asylum-seekers who enter the bloc from mid-March 2017 onwards through Greece and make it deeper into Europe.

Avramopoulos acknowledged that numbers of returnees were likely to be very small as Greece also needed to give individual assurances of proper treatment and the most vulnerable - including unaccompanied children - should not be sent back at all.

The bitter disputes between member states over how to cater for the migrants remain unresolved.

A deal on migration in March between the EU and Turkey has slashed new arrivals, with the Commission saying fewer than 100 people a day were making it across to Greece compared with several thousand at the peak of the influx.

But that deal looks fragile due to a worsening of ties between the EU and Turkey over Ankara’s crackdown in response to a failed military coup in July.

Meanwhile, under a plan that was supposed to cover 160,000 people and which expires next September, fewer than 8,200 asylum-seekers have been moved from Greece and Italy to other EU states.

Avramopoulos said he hoped everyone eligible would be relocated by September.

Obligatory quotas on refugees are one focus of the dispute between EU states as they seek to reform their common asylum rules.

Brussels, Berlin and Stockholm, among others, insist on a well-defined mechanism to share them out. Warsaw and Budapest are among those that say they will not be forced to take in any.